Is it professionally viable to leave an American math PhD program for a Master's in Germany? Background

I'm an American who will be starting a pure math PhD at a relatively prestigious US public university later this month (I realize that it might seem pointless ask a question about a program I haven't yet begun; however, I think that my question is basically independent of these concerns.)

Moving to Europe is one of my goals in life (just to clarify, it has been since before 2016), and while applying to grad schools I seriously contemplated studying in Germany. However, friends and former professors, as well as professors from my current PhD program, with whom I spoke while visiting, advised me that it would likely be much easier to find a research job if I completed a PhD from an American university. Based on this advice, I accepted the offer from my current program.

It seems to me now, however, that this advice is likely false—while I have heard that German academia is considered to be quite closed to outsiders, it seems that there are quite a few mathematicians with PhDs from German universities who have acquired desirable research positions outside of Germany, and my impression is that a PhD from a well-regarded German university is quite competitive on the international and the European job market. Moreover, it seems questionable to me that a PhD from a moderately/relatively prestigious American university would give one an edge in the academic job market outside the US (perhaps I'm wrong, here, though).

Given this situation, I am considering applying to a Master's program at a certain German university which is quite strong in my area of interest, and
 which also seems to have some connections with my current program (in terms of research collaboration), with the intention of completing a PhD at the same university afterward. In terms of personal preference, I would (based on prior experience) much prefer to be residing in Germany, so continuing on at my current program doesn't seem appealing if it's not likely to be more advantageous in terms of finding a job in Europe after finishing my PhD.

Questions


Is it likely that leaving my PhD program for a Master's in Germany after a year would damage my career prospects?
In this or a similar set of circumstances, is it possible to leave one's PhD program without burning bridges completely?
Is it likely that leaving my PhD program for a Master's in Germany after a year would damage my career prospects?
  


Yes: A Master's degree in Germany is considered by many people
 (and pretty much everyone over 50 or so) to be baseline education: In other words, it's the bare minimum you can have and expect to get a job in a relevant field. Yes, the times, they are a-changin', especially in e.g. software development, but "only" having a Bachelor's is still something of an anomaly: The Bologna Process has changed the structure of German university education but has not (yet) changed German culture and expectations.

Therefore, you'd be going from a culture with relatively lower educational expectations (the US, where a Master's degree hold a lot of weight and a PhD even more so) to a country with higher expectations and you're going down one educational level.

Likewise, it's possible that a well-known PhD program will be acknowledged in Germany in relevant field(s), but there are fewer German universities that are so amazingly well-known that they're acknowledged in the US. After all, the US is about the size of all of Europe, so it makes a bit of sense that the US is more insular than Germany is.


  
  In this or a similar set of circumstances, is it possible to leave one's PhD program without burning bridges completely?
  


It isn't exactly the same as leaving to get a Master's somewhere else, but it is possible that you could work on building a relationship and rapport with groups in Germany which do work similar to what you do and then ask them if you could spend some time there as a visiting researcher. This way you'd not burn bridges at your current department while still allowing you to experience how it is to live and do research in Germany. Also, you'd end up with a PhD in the end rather than just a Master's, which would make it much easier to move to Germany after the program should you wish to do so.