The article in the German Wikipedia (for some perhaps telling reason its title refers to "uprising" vs. "genocide") mentions pressure exerted by protestant missionaries' churches ("Der Druck der Öffentlichkeit, besonderes der evangelischen Missionskirchen, wuchs.")
It quotes a German PhD thesis from 2004 that provides further information (e.g. on page p. 182). It includes a detailed account of the battle of Waterberg and its tragic aftermath in the Omaheke desert. It also confirms Lothar von Trotha's harsh individual stance and imposed methods but also mentions protests from his staff and that some (sadly few) Hereros made it through the Omakehe desert alive.
In terms of public outcry in Germany, it points to activities by the "Rhenish Missionary Society", which led to a reaction by Chancellor Bernhard von Bülow and to von Trotha's recall from colonial service and return to Germany in 1905 (translation courtesy of Google here):
Insbesondere die Rheinische Mission bemühte sich um eine Befriedung
des Konfliktes und verhandelte mit dem Auswärtigen Amt und dem
Reichskanzler in Berlin. Dabei kritisierte sie in aller Schärfe von
Trothas Proklamation. Pastor Hausleiter von der Rheinischen Mission
bat Reichskanzler von Bülow in einem Schreiben, Missionare zu den
Aufständischen zu entsenden, um diese zur Übergabe zu bewegen.
Außerdem sollten sich die Missionen um die Alten, Kranken, Frauen und
Kinder kümmern sowie Zufluchtsorte für diejenigen Herero aufbauen,
die zwar am Aufstand nicht aber an den Mordtaten gegen Weiße beteiligt
waren.
Again, there is a bit more further information in a German-language diploma thesis from 2010. It analyses the Rhenish Missionary Society's publications from the time (and seems to arrive at or start from a more skeptical view as to the alleged importance of the society's noble role as viewed or presented in retrospect from a "white" angle.)
BTW, whether this was "genocide" or not, von Trotha would not have been able to pursue it after 1905 (e.g. up to 1907 as implied in the question), for 1904 was the year of the incidents and 1905 was when he was transferred. The 1911 Encylopaedia Britannica, not always a reliable modern source on colonialism, gives a (to this reader's eyes) relatively fair account of the main actors involvements, but adds some own confusing language ("concentration camps were established in which some thousands of Herero women and children were cared for").
Further evidence could perhaps be recovered from German newspapers at the time (e.g. a Vienna-based newspapers provides a free online archive going back to 1848). However, I currently do not know any such source with a convenient online index. It also seems as if Ludwig von Estorff, one of the officers who tried to stand up to von Trotha in 1904, later had books published about his time in Namibia: They are (sadly) out of print by now.
UPDATE: Paul Rohrbach's book Aus Südwest-Afrikas schweren Tagen (1909) is a collection of diary entries from 1903 to 1905. During that time the author was a senior official in then German South-West Africa. He mentions the Rhenish Missionary Society several times in passing but not in a way that would suggest his own affiliation. There also frequent references to the "Siedlungsgesellschaft". The report reveals a perspective observer and able administrator, even with a sense of humor (translation courtesy of Google):
Herr Schmerenbeck meinte beim Einreiten, als wir alle großen Durst
feststellten, daß irgendwo in einem Zimmer noch eine Kiste Bier stehen
müsste. Statt der Kiste fanden wir in dem betreffenden Raum aber einen
kleinen Termitenbau, und als der mit der Schaufel
auseinandergeschlagen wurde, fanden sich auch ca. 20 Flaschen Bier
unversehrt darin vor. Die Termiten waren ins Haus gekommen und hatten
die Kiste samt den Strohülsen der Flaschen rein aufgefressen. Es ist
wirklich wahr: nur Glas und Metall sind vor ihnen sicher. Aber die
Flaschenkorken? An die hatten sie wegen der Stanniolhülle nicht
herangekonnt.
With respect to pressure from public opinion in Germany it may be relevant that Rohrbach throughout his tenure seemed concerned about a general lack of interest in the colony's fate back in the home country: this would seem to suggest there was no proper basis for raising a broad opposition, e.g. due to lack of information.
Rohrbach mentions and severely critizes General von Trotha several times, although he mentions the "genocide" incident only once in passing and regrets a fifty percent mortality rate. While he exhibits many European prejudices opposite Africa that were typical for his time, I find it very hard to believe that he "was an advocate of eradicating native Africans in order to make room for German colonists", as was mentioned. The following excerpt (allegedly from the June 19, 1904 diary entry) may sum up his views as good as any (again, translation courtesy of Google):
Wir alle haben nun die Furcht, daß der Übergang des Oberbefehls an
einen General, der nie in Süwestafrika gewesen ist, zusammen mit der
fortdauernden notwendigen Vermehrung der neuen Truppen und Offiziere
eine Art von Kriegsführung hervorbringen wird, die unseren
Bedürfnissen wenig entspricht. Was von den Reden bei der Aussendung der
neuen Truppenverstärkungen aus Deutschland verlautet, und was hier
über Äußerungen Trothas gleich in den ersten Tagen seines Aufenthalts
im Lande kolportiert wird, gibt, fürchte ich, nur Grund zur Sorge. Es
ist viel zu viel von der "Vernichtung" der Hereros die Rede. Das hieße
auf das Übel des Aufstandes ein zweites setzen, das schlimmer ist
[...] Die Hereros führen einen Freiheitskrieg gegen uns, und sie
führen ihn in der Art afrikanischer Barbaren. Auch die Cherusker
sollen den römischen Sachwaltern nach der
Varusschlacht die Zunge
ausgeschnitten und den Mund zugenäht haben -- und das waren unsere
Vorfahren.
Rohrbach's book is an interesting read and made me think that Karl May may perhaps have had him in mind as a model for his various (from a modern view also more-or-less tainted) fictional heroes.