Russell.

Very much doubt that a rubber layer built-in in the doublers would do a single thing. It sounds like a lot of effort for little likely return.

Some Fox engines softened up their vibration as they got time on them (slant plug 1970's 29 and 36, for example), or we just got used to them shaking...

Strong front end on the model would help...

Make blessed sure the prop is VERY well balanced.

Possibly adding a head gasket, or even two, might soften the  combustion.

Don't run the engine "hard" - find a setting that is near, but not at, totally peaked out - or if you're looking for a smooth 4-cycle to get a 4-2 break, I don't know if this engine is timed/ported to make that easy.

Use a somewhat lighter prop load - say 9-6 or 10-5 instead of a 10-6. It may be happier in easy-wet-low 2-cycle all the way with a flatter pitch prop, even a 10- or 10.5-4.

If fuel has any effect, a 10%nitro, (at least) 25% CASTOR oil fuel may be kindest.

I've flown it now, that was a big event, by the way.  It's been a long time.  The engine ran fine and didn't seem as rough as on my bench setup.  Guess I'll have to remove the rubber layers and try it again so I have something to compare with.