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I had a similar problem and used fiberglass resin. I outlined the dead sound area to get a picture of the void. I drilled a minimal amount of holes which sstill seemed like alot, I mostly wanted to see the resin when squirted in one hole, come out of another. To squirt the mixture in the hole, I purchased a few squeeze bottles from local hobby store (Hobby Lobby). You can actually easily reuse the same bottle after mixture cures. Once I got the area filled, I would immediatley put tape over the holes (lowest holes)so the mixture did not run out until I was ready to start the squeezing, dispersing and clamping. that made it a little easier to work it into the voids. At the end before the final clamping I gently squeezed the excess to the few holes remaining open(no tape).
The other handy tool I founf was at Harbor Frieght, they have for a few dollars these very large vise grip style clamps, http://www.harborfreight.com/cpi/ctaf...mber=39535 They came in a pack of three but greatly help clamp the deep area.
Sorry to get long in the tooth, I just thought I might share one or two things that helped me.