What was missing? Rejected by 6 out of 7 schools

PHD or Post Doc in the US is a great idea!
An issue is that US PHD’s presume research experience, and it’s not easy to get (if not downright impossible) in Germany, not because there’s none (of course not), but because paths are very fixed and those involved are doctoral students and, to a certain extent, Master students (Master2 students all do, although not always significant/meaningful.) It’s a handicap that’s hard to bypass. A Medical student may be able to do research in his/her last years, I don’t know, but I have heard complaints about how comparimentalized the training is, so that you’re not supposed to be both MD and PHD. MD going on to PHD certainly happens, but I don’t know the process, as it doesn’t seem pre-planned like in the US. If it does exist, all the better for the OP, but OP will need to look it up.
Since 1’s are exceedingly rare, OP’s likely to be a top student in his class, so by knowing what to target he’d have a good shot at reaching his goals.