The D# is labeled so in the German6 becuase altered notes resolve in the direction they are altered, so that's why we call it D# vrs Eb. So yes your point is valid (Maj #6). I am not going to argue this point w/you (maj#6 vrs Dom7). I did not invent this theory or coin the terms G I F augmented 6th, I am simply regurgitating classical theory. The augmented 6th chords are definetely not a high point of classiscal theory, and I think any theorytician will stand by that pt..However, they are an excepted form of reference/analyization and I would encourage you to investigate them farther before disputing there historical relevance to modern theory.
The quote I posted on this subject I think sums up quite well theoroticians view on classical augment 6th chords.