I like the dog bowl resonator! That could work well as your diaphragm. It's relatively light weight and rigid, like a speaker cone. It could push some serious air.
But, like we talked about above, the diaphragm has to have some vertical travel, in order to do its job. You can't just set it on the body with the outer flange right on the wood. Like it is, all you'll get is a really high pitched clanging sound, like you were banging on the dog dish with a spoon. Not a bass at all.
What you need is a "springy ring" around the flange, between the flange and the body, so the whole dog dish can move up and down. One idea would be to use some heavy black foam weatherstripping, with the adhesive back. Stick a ring of that around the underside of the flange of the dog dish. Maybe rout a little rabbit around the hole in the body, for the foam to seat in to? But make sure that the dog dish is floating on the foam, and can't rattle against the wood. Or, instead of the foam weatherstripping, maybe a ring of rubber tubing? Or a large diameter soft silicone rubber O-ring? Again, the idea is to allow the whole dog dish to be able to bounce up and down, to pump out that low frequency sound.