I am just going to respond so Ben can get some sleep.
Well, in your example group 1 and 2 don’t overlap at all. The thing to remember is that the decision to center or not-center is not a model level decision but a parameter level decision. That is, you could do one parameterization for some groups and another for the other groups and that could be the optimal approach. It would be unwieldy obviously. I only realized this after this comment by Michael Betancourt. If you really want to get into the details of when to use which parametrization Michael’s paper with Mark Girolami is my go to guide.