I agree with your assessment that more wood will deaden the sound, but if there's no part of the frame directly contacting the cushions, you may need to build something similar to what others here have.
I checked, rechecked, double rechecked, and checked again the wiring. It's sound as a pound.
The shakers are shakin', but the movement wasn't being transferred to the seats they way I had them mounted at first.
I don't really know how to describe this, but it looks as though the only contact the cushion makes with the frame is at the topmost part under the armrests, under the knees, and at the top of the backs. Maybe that's standard, but it looks like the seats themselves are sort of "suspended".
It's a well-made sofa set, but not terribly high-end. Maybe I'll try and post some pics, if you guys would be so kind to help out. My camera is only 2.0MP, though, so they won't be the greatest resolution.
Maybe I just need more shakers, and more power...
Seriously, it could be this amp. I know it's a piece of crap, really, and that is probably the real issue.
I'm going to try the first remedy I posted, i.e., a wood "bridge" to which the shakers will be mounted. I still think some type of metal brace or bracket would be better, though. I'll let you know how that works.