Warning: Mach’s Principle is not experimentally proven, though it is widely considered to be credible.
I don’t see what experiments have to do with anything so long as we all agree GR is true. Apparently there are a lot of different things that people have called “Mach’s principle” and GR obeys some of them but not others: http://arxiv.org/PS_cache/gr-qc/pdf/9607/9607009v1.pdf . For example, it seems like you want to claim “Mach7” from this paper (“If you take away all matter, there is no more space”), which is false. It also seems like you want to claim “Mach10”, which is meaningless in GR. There’s a thing called “Goedel’s rotating universe”, so clearly there’s something subtle going on.
Also, I think where you say “centripetal force” you mean “centrifugal force”; they go in opposite directions, the centrifugal (pseudo)force is the one pulling things apart, the centripetal force is the one keeping things together.