I really sympathise with your frustrations John, in particular because of my vehicle refinement experience to which I alluded in my previous post.
Whilst it may seem odd that your experiences with your 987.2 Cayman and 997.2 911 are very different, and although both vehicles share the same body structure, steering and suspension components forward of the A-pillar, the rear suspension layouts are very different - strut versus multi-link - with the 911 having different [more?] attachment points and therefore different [more?] potential sources of force input due to road excitation. Whether or not that’s the reason for the differences or if the different tyres are playing their part is an open question.
Unfortunately I think that your only course of action is to try different tyres from your recently fitted P-Zeros, at significant cost, although probably you could sell your lightly-used tyres. However, although you’d need to look carefully at potentially different wheel offsets to avoid fouling the wheel arches, it may be possible to swap the 911’s wheels for those on your Cayman to evaluate the Michelins on your 911.
There’s also the open question of whether or not using N-rated tyres will make any difference since they will have been developed specifically for your cars, perhaps taking noise into account, and you haven’t indicated what you’re using on both cars. Note also that although new tyre labelling includes exterior noise produced it doesn’t necessarily mean that a lower value will mean that it will be quieter inside the car.
Jeff