What do the experts think?
Why is centring a piece causing you so much trouble? (A picture would help)

If you're using an independently jawed chuck for accuracy you'll need to dial it. One can usually do it by eye to about +/- 20 thou", just using the concentric rings. It should only take a few minutes to get the TIR down to 1 thou or so.

If you only need a rough centre ~0.003" then a self-centring chuck with 3,4 or 6 jaws would make your life a whole lot simpler.

I'd guess your plate Idea would work to say 0.01" (if you're lucky ;)) tightening one jaw can throw the reading off by that much.