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Thank you very much! These are very helpful and plausible explanations that I had somehow overlooked. You have made me revise my thinking.
I now believe that the name beginning as Dauber would not have evolved much over the years. At least the vowel sound would have remained essentially the same, and would not have evolved into the variations that reflect the presence of the umlaut (e.g., Deibert), because there would be no tendency to make this shift from the German "au."
On the other hand, Tšuber could have evolved in two different directions: (1) The Palatines themselves pronounce the German "šu" like German "ei" (as I explained earlier), thus accounting for variations like Deibert. (2) But those without knowledge of German have always tended to omit the umlaut, which could easily have led to evolutions like Tšuber -> Tauber -> Dauber.
To sum up, I think any variation that reflects the presence of an umlaut is likely to have started out as Tšuber, whereas the variations without the umlaut may have started as either Tšuber or, what is more likely, Dauber. I have been so caught up in analyzing the shifts, I wasn't considering the possibility that Dauber simply started out as Dauber in many cases!