Sometimes when I overanalyze something, it is because I am avoiding the obvious, my own feelings. Feelings and having them are what make us human. So what is best for you and your ability to handle things is what prevails. We are all wired differently in terms of coping, strength, emotions. It is easy to get stuck on a label to explain ourselves when that is just one piece of the puzzle.
I don't know your situation in detail. Maybe look at the pros and cons of saying goodbye. If you can do it and will feel better for it then I don't see why you couldn't. Sometimes the simplist ways of communicating are the most effective. Or you can write him when you are settled in the new town. Or not. If it will make things harder for yourself then don't say bye. Protect yourself.
You should listen to your feelings but analyze them with your rational brain to see if acting on them will do more harm or help. When I am overthinking something (a feeling). I know that isn't the time to get a clear picture for myself. I wait until I am in a relaxed state, with some distance and then see it clearer.
I know this answer sounds vague but I guess I'm saying to not analyze with emotions your emotions. Feel them, acknowledge them, then filter those feelings with your calm rational side.