(Sorry for the long question in advance! If it's too long, you could skip the first two paragraphs.)
I'm currently enrolled in a PhD program in a relatively prestigious school, which is very well-known in my field and in the specific area I'm interested in. Despite the department being a very good match for my interest, for some very personal reasons, I really need to move to a different place. (I assure you that my reasons are absolutely convincing, but unfortunately are too personal and complicated to explain it here, so I'd appreciate it if you could suggest answers to the question I'm asking and not discuss whether I should change my mind about leaving my current program).
Before I explain where in the application I could get into trouble, I need to say, that I can't explain my reasons for leaving my current university to my professors. Although the reasons are not at all about the department (I'm actually pretty happy with the program itself), and are only related to the location, since understanding them requires some background on what my reasons are about and some familiarity with me at a personal level, I have very little hope that they could actually sound convincing to my professors. They're the sort of reasons that I could explain to a friend and I'm quite sure they'd find them absolutely convincing (as those I explained to did), but I can't explain it to a colleague or a professor unless I establish some level of friendship with them beforehand. So, I prefer to reserve that option as the last option.
Although I'm trying to go and continue/do my PhD somewhere else as soon as possible, I'd want to do that next year if my applications weren't successful this year (especially because next year I'll have more publications, could possibly get a little closer to my advisor here so I could get their help and explain my reasons to them, and will have a higher chance in general). That's why I don't want to jeopardize my current position at all, because I might end up staying here one year longer. I'd appreciate any suggestions to solve the problems explained below.
I would consider my problem to have two main parts:
Since I'm going to apply for PhD positions, mostly in Europe, but possibly a few in the US, I need to contact potential advisors (in most of the programs I'm considering, the department-level admission is almost just a formality and any PhD student has to be accepted by the advisor first). I'm afraid that the prospective advisor might know a professor from my department (especially because they work in the same field and my department is very well-known in the field), and they might contact that professor and ask about me, which could get me into trouble in my current program (possibly resulting in the school cancelling my scholarship). I do try to make sure that they haven't published a paper together recently, but sometimes it's hard to figure out for sure if they're collaborating on a project at the moment or not, or if they're going to meet at a conference soon.
It could be difficult to justify why I want to leave this department given my interests. The department is a great match for my interest and I'm assuming that whoever reads my statement letter is not going to ask "why won't you complete your Ph.D. with prof. X or prof. Y at your own department then?!". Any suggestions on how to minimize the amount of annoying personal explanations, while trying to explain why I want to go somewhere else?
I'd greatly appreciate any solutions you'd suggest. Also, do you think these stuff are actually something to be worried about or am I just overthinking it?!