Post-doc applications
One of the biggest reasons for moving around is so that you learn, over time, a variety of techniques and viewpoints. If you stay in a place too long as a student, you may already know whatever it is that they are able to teach you. 

But that isn't your situation. You are moving to a new situation within the university, broadening your horizons with these other people. My guess is that it would be good to take advantage of the situation. You also, as you say, seen a variety of different faculties already, so it is less important to move on than if your education had all been in one place. 

Don't stay forever, of course, but learn what you can from the people able to give it.