It appears that that geographic isolation was a fairly effective barrier, and I find little mention of foreigners living in the New Mexico region.
A couple that are mentioned are noted in The Works of Hubert Howe Bancroft: History of Arizona and New Mexico. 1889
In 1804 William Morrison of Kaskaskia despatching the creole trader
Baptiste Lalande up the Platte instructed him to carry his goods to
Santa Fé with a view to test the commercial prospects in that
direction Obeying his instructions Lalande succeeded in being arrested
by the Spaniards and carried to the capital The New Mexicans liked the
goods and Baptiste liked the country so well that he resolved to
settle there and even omitted the formality of accounting to Morrison
for the consignment. In 1805 James Pursley a Kentuckian who left St
Louis three years before after many adventures among the Indians was
sent by the latter to negotiate for Spanish trade and after succeeding
in this mission he also settled at Santa F é working as a carpenter
Another foreigner is mentioned in relation to Zebulon Pikes mission into the region:
Baptiste Lalande and another Frenchman tried to gain Pike's confidence
but were regarded by him as spies. Solomon Colly one of the Nolan party
was living in New Mexico and served as interpreter.
Spain was more likely to arrest foreigners who did manage to cross the unwelcoming wilderness separating New Mexico from the rest of the (non-Spanish) world.
Moved by Pike's account of the New Mexican country and entertaining an
idea perhaps that Hidalgo's revolution had removed the old
restrictions on trade Robert McKnight with a party of nine or ten
crossed the plains in 1812 and reached Santa Fé The result was that
their goods were confiscated and they were arrested being held in
Chihuahua and Durango as prisoners until 1822 when they were released by Iturbide's order.
The short period between Mexican independance (1821-2) and the Treaty of Guadalupe Hidalgo(1848) did provide a loosening of the Spanish restrictions on trade, and again Bancroft mentions a few trading attempts in this time:
With the independence of 1821-2 the Santa Fé trade proper -legitimate
but for some liberties taken with Mexican custom-house regulations and
unobstructed except by difficulties and dangers of the journey across
the plains, may be said to have begun and it will be a prominent topic
of later annals. Captains Glenn, Becknell, and Stephen Cooper were the
men who in 1821-2 visited Sante Fé with small parties making large
profits on the limited quantities of goods they succeeded in bringing
to market and laying the foundations of future success. About these
earliest trips we have but little information except that the traders
uncertain as to the best route endured terrible sufferings from thirst
Becknell made two trips Major Cooper still lives in California as I
Write in 1886 and from Joel P Walker one of his companions I have an
original narrative of their adventures
This notes (emphasis mine) the difficulties on reaching this area. This is much different than the relative ease of reaching the shores of California in a ship loaded with trade goods. I think this geographic isolation, as you mentioned in your question, severely limited the exposure of this region to foreigners and their influences.