So I forget exactly who said it, but in one of the many vibration threads someone made a note about how "maybe a little more mass helped stable out the APM". Now I know there are some neat rigs out there but I want things simple, so for a simple test, I took the heaviest small item I had lying around, a ~90gram foil pommel, and just taped it to my APM.
The results were good. I think a properly sized and fitted plate, maybe on the bottom, would help a lot. Again, I just stuck the weight on there, in the only way it could fit, this was a crude test, but I think it has merit.
(The APM is has two pieces of moon gel between it and the frame and it's secured with a piece of velrco.)
Before: I was +/- 5-6 with a greater min/max change.
After I was +/- 3-4 and much smoother.