This is a bit of a silly question that will need an explanation of the background that motivates this question.
Background. I met a man named Andrzej. He was called approximately An-jay /dʒ/, or rarely Andre(y) under influence of the respective speakers' native languages, ie. /dʁ/ for German or rather /dɹ/ for one guy from Nebraska. It took a moment of explanation, although I had learned about Polish -rz- not too long ago. Subjective perception, expectation and noise surely played a role in my misunderstanding, since German /ʁ/ may cover a wide range of realizations, so I was probably the only one who actually heared and said Andre up until that point.
The American pronounciation was still irritating, so I coopted the fully English variant /ˈæn.dɹuː/ in jest and confered with the mate who thought I did this in bad faith, implying he intended to approximate the name rather faitfully without rhotics. Nevertheless there is hardly any audible difference to me. I kept trying to imagine the trill ~ tap that must have been there once upon a time, before the sound change completed to /dž/.
Question. How far off am I on both accounts concerning the archaising pronounciation and the American ones, whether rhotic or not. Or in other words: How far are their developments comparable, if not related by common drift?
In hindsight I imagine that a tapped stop gave the impression of rhotacism. (I'd simply ask, what's going on here, but the given information might leave too much up to speculation).
A pro pos. This question is following @Draconis answer to /t͡ʃ/ vs. /ʧ/ vs. /tʃ/