Cans of high expansion foam, from the big boxes store, isn't very expensive so you could seal it up and go for it. You want to keep the foam confined to increase the density.
If you go this way it will be hard to add anything else because of the lost space.
GM, Fisher Body, use to glue wood blocks to frame and body to do the same thing, I've never seen any on the frame but was told that this happens. The one I saw were on the body panels.
The foam approach does work. We installed a 30" hollow tapered Al mast, a light pole, on a 46" boat that had the same problem, it vibrated, bad, around the optimum cruising speed. We changed all the stays, no help. Went to pipe stays again no help. I was checking out an insulatin job at the fish house on day while they were foaming in a new freezer. A quick discussion and assurances that the density of the foam could be raised we fill the mast with the foam through 4 holes. plugged the holes with taper pins and let the foam expand. After the expansion the mast would hardly ring sitting still and not a vib while running.
Brain thing:
Just a though find you an old piece of frame ring it and fill it with the highest density foam as possible. After the foam expands ring it again. A little work, but it might tell you something. Maybe a yea or nay.