The question can be put like this:
In case the "immigrationist theory" is true, how did Romanians/Vlachs became the vast majority in Transylvania?
The simplest answer is that there were too few Hungarians there when Romanians (slowly) arrived, that not many (Hungarians) came and stayed after that, and that those who did come to stay moved slower than the (slowly migrating) Romanians; if Hungarians were a majority at some point, too many of them left and/or too many Romanians came to stay.
Can it be so simple?
An odd thing here is that we have a fact ("Romanians/Vlachs became the vast majority in Transylvania"), a theory ("immigrationist") that is supposed to explain the fact, and a question that asks how is it possible to go from the theory to the fact. The relation between these elements is already rather obscure. Wasn't the theory itself supposed to give the answer? What other use it may have then? Possibly the OP has "adopted" the theory in spite of this, for other reasons than its explanatory value in relation to the facts, probably because it seemed preferable by comparison to other theories. (Although I even suspected him for a moment of cunningly formulating an argument ad absurdum against the "immigrationist" position. I don't know if he is aware that his question can be played like that too...)
But do we really need such theories? Do facts need theories? Maybe descriptions are preferable, that is clarification of facts, context and concepts.
If the answer seems so difficult to provide, couldn't it be that the problem lies with the immigrationist theory? Not in that it talks about migration, but in that it involves the need for a theory. It is this need that induces a mystery. Without it the answer would be so "simple" that it would cease to be sought for its "theoretical" value (position within a theory or another) and would be appreciated for its virtues of simplification and clarification, as a good description.
"Continuity", on the other hand, seems to me less mysterious, but still obscure and in need of clarification. I think that the only material proof present is the Romanians themselves, their language and their location on the map. But that is the fact itself, not a justification of facts, which is not needed anyway. "Continuity" should not be seen as a hypothesis, an explanation for a fact we investigate, as it represents the very fact that needs (or not) to be explained. That we cannot explain it doesn't mean it has thus become more mysterious than before, doesn't mean we cannot see it as good as before, and doesn't force us to enter even darker corners. If I don't know how a thing got here I am not forced to say that it shouldn't be here, that therefore it must come from a different place and that I must find what this place is. It might be more economic to say that because we cannot say how it got here, it maybe that it was here in the first place, or something very close to that.
If we have to imagine something rather than nothing, I don't think that it is harder to imagine the continuity than the migration.
Personally I find even more difficult to imagine:
a Latin-speaking population starting to migrate up and down (or mostly up), and especially migrating outside the empire; is there another case in Europe of a Latin speaking population (originating from the Roman empire) migrating like that?
a population migrating from south to north (or SW to NE) when most of the population movement then and there is north to south (or rather NE to SW); how come those people were going where everybody was fleeing from? and how come they stayed in a place where nobody else wanted to stay (given that the aforementioned population finds itself in majority there)?
a migration that is extremely slow compared to all the other migrations that took place, one that never amounts to an invasion; are there other cases in Europe of such phenomena?
a Latin-speaking population migrating at a very low speed not only in an improbable direction to an improbable place, but, of all the improbable places up north, to the precisely one place that had been previously occupied (and that the concurrent theories say it never left);
I can imagine a migration that is so slow and discrete that amounts to a sort of geographical cross-Danube continuity, close to the "admigration theory", but that seems to me another name for no-migration.
The empire was on the defensive and no (other) such Roman invasion/occupation of territory and assimilation/outnumbering of the population already occupying it can be documented. On the contrary, the general scenario of all other neo-Latin countries fits here rather well: a Roman population militarily and politically subjected by invaders that adopt the neo-Latin language. As for the mystery of the adoption of Latin by the local population in less than 200 years of direct Roman rule, maybe it can be explained - or, even better, described, because a good description of facts may be enough - through the aforementioned cross-Danube geographical continuity - after the Aurelian transfer to the south and during Byzantine and Bulgarian empires presence on the river.
There is a logical (or philosophical) problem (or illusion) here, something like a wittgensteinian "mental cramp" that needs soothing: theories or explanations can be more or less probable, but a fact (Romanians in Transylvania and on the whole territory of Dacia) cannot be probable or improbable. It seems to me that sometimes this discussion is opened in a context where the probability/improbability of explanations contaminates the description of the facts as facts. It's the theories that need justification, not the facts. - That is, in a rational and scientific discourse; in a political discourse, it might be the other way around (as the scientific gratuity of a theory can coincide with its political "utility").
Not only the "immigrationst" theory (favored by the Hungarian nationalistic discourse) can be affected by the "mental cramp" of fact-justification; the "continuity" theory (favored by the Romanian nationalistic discourse) is affected too when the Romanian population (the "fact") is seen as a proof of historical continuity from a start point of "origin", which in turn is seen as a justification of the initial fact. All this is circular, a logical trap that can be by itself tempting, but is also favored by affective/political/moral context.
I think that the question itself can be completely disconnected from the "immigrationist theory" (and from concurent theories as well), even though without theory much of the mystery is lost.
Why haven't Hungarians colonized Transylvania more densely when they could? why haven't they anticipated the possibility of finding themselves one day an ethnic minority in a province they had dominated for almost a millennium?
I can try some answers but they are all very modest:
- in spite of what some Romanians like to think, the Dacian/Romanian teritory was not really a magnet for everybody; it was attractive enough for some people to come but not attractive enough for most of them to stay; when counting ethnicities came in fashion, Romanians (that is the people who somehow got there, spoke neo-Latin and didn't leave) found themselves a majority;
- like other invading powers, when Hungarians came to Europe they pushed West until they were stopped, and then they settled in Pannonia; a movement to East was contrary to this trend; they initially administered Transylvania, Moldavia and even Wallachia as merely marches facing Eastern threats;
- at least for Hungarians and at least Transylvania was not attractive enough; they had plenty of grassland in their flat part of the country and it's that what they preferred; (in the map below: Transilvania is populated in majority by Romanians but it is the least populated part of 1910 Hungary);
- until recently nobody was thinking in terms of ethnicity, or if they did they were never in charge of affairs; somebody was populating those areas, and they did serve the King of Hungary and the Prince of Transylvania and ensured access to the country's resources.
- Edit in response to comments by JohnDee:
I think the OP is looking for an answer, not just a discussion (in comments). The question reflects a sort of philosophical wonder in front of the facts and is related to the larger mythological problem of "origins", the root-idea that we have a need for theories of origin. This can also be related to the 'mental cramp' already mentioned: as theories need rational justification (arguments), facts are also imagined as "in need" for something similar, a fact-justification, an odd role that can only be played by an "origin". I find interesting to see that questions can get answers in the absence of that need.
Personally I tend to prefer "continuity" because it seems to be "closer to facts": not in the sense that facts are in its favor, but that it is "closer" to being a description of facts more than a "theory" (a description of relations between facts, and even between facts and their origin). I find that more "economic": lesser assumptions that entail fewer further explanations. - Simply put: a "theory" should not provide more questions than answers.
To give an example of how the "immigrationist theory" can entail farther need for explanations: if arrival of Romanians in Transylvania needs explanation, the same is the case in the territory of their own two Valach/Wallachian provinces, Wallachia and Moldavia. Those must have been populated by Romanians that came from Transylvania at a later date; their territory must have been either almost completely empty, or populated by Slavs and/or other people that became not only a minority but were completely assimilated by the newcomers. - If nobody populated those territories before, why is that? and why only Romanians did? If they were populated already, why were Romanians so good at imposing and preserving their language when they lacked political institutions of their own?
The post is already too long, but I fear the OP (given the comments made) may not find it clarifying enough (or interesting enough to read). I fear such clarifying discussions tend indeed to become very complex (but there is no point in being apologetic about that, as I think rational tension is the only alternative to the irrational one).
On the other hand, I need to prevent further misunderstanding on the point of personal sympathy or inclination towards one theory or the other (and I do not wish post or comment any more) by underlying that:
I very much doubt that what is called "theories" in the question and answers here can really be considered such in the proper (scientific) sense; the term can only be used by a loose analogy and for the sake of discussion; they are rather "facts" themselves, namely historical facts of the 19th and 20th centuries; these "ideas" have been thrown in an arena that had nothing scientific about it, and they look flimsy when taken out of there with a scientific grasp;
If considered as real theories (meaning they should favor understanding, better description and clarification), they are not equal; I think that we clearly have two extreme theories that exist more by historical than logical necessity (immigration vs historical continuity), and a third middle theory which was constituted as an ad hoc effort to avoid both the political and the logical problems of the other two: the geographical continuity (or the admigration theory), which, as such, seems the most reasonable one;
I find it more useful in any case to emphasize the very problem of the utility of theorization than to adopt a theory or another; but when these theories are opposed and arguments are presented in favor or against one or the other, that shouldn't be seen as personal sympathy but merely as back and forth movements in a detective-like effort of drawing a more detailed and clear picture.
I really think the "historical continuity" is a trap, so that one may be tempted to jump to "immigrationism". But that's like jumping from the frying pan into the fire (or "from the lake into the well" as they say in Romanian): for one anti-continuity objection you can find two anti-migration ones. That is because the more we improvise theoretically in response to a pre-envisioned theory, the more hypothetical facts are imagined that cannot be explained. This whole network of theories involved here is a larger trap, a net from which we have to cut loose in order to even think clearly.