I'd be surprised if that does the trick. It depends on the frequency. If you compress and tie down a bunch of it into a dense springy mass between the speaker magnets, it should absorb a certain level of any frequency. If it's not dense enough, it may have no affect on the booming frequency at all. Places like Target also have Polyfill pillows very cheap. I'd say you'd need maybe a few of those worth. You might have enough already. The bigger the dense mass, the more bass level reduction. If you were to pack tight the entire cabinet, it would likely be lacking in bass. So, you can control the entire bass response in that respect.
Say, I was hoping to catch you before you spend time gluing in the Polyfill. I've learned a good deal about audio and physics basics since the early 70's, first from my internationally renowned physicist father, and electronics genius step-father (who designed a circuit board for a competing artificial heart). I've also learned some important audio specific physics basics from a legendary Boston area MIT grad audio pro. I've since taken an acoustics physics course in college and have learned some valuable things since in my personal study/research and from the late Bill Lawrence (aka Willi Lorenz Stich).
Point is, I don't know who told you that 1-2” of loose Polyfill on the cab surfaces would damp bass resonances, but they are mistaken. 2” of Rock Wool is required to damp ~200Hz, and 4” for ~100Hz. Rock Wool absorbs much more bass than loose Polyfill, which the big bass waves will go right through. The Boston Audio Pro fella was the one who recommended tightly packed Polyfill. The physics makes sense, and I've tried it on home audio speakers. If it's not packed tight enough though, it may not absorb the Fr (Frequency resonance) in question. Ideally, the wad should be about as dense as memory foam, but elastic like rubber.
Another option is based on the idea that a non-porous highly flexible/low tension/low elasticity plane roughly the size of the vibrating surface area should be an ideal bass dampening solution. A great material for that purpose would be this stuff:
http://www.homedepot.com/p/Roberts-100- ... 5yc1vZbejl
I have some of it and it has the right internal dampening properties. I'd think one freely hanging sheet should do it, but you can add more layers with some space between them if needed. Probably staple and duck tape it to the top with ~2” gaps around the edges would work best, so it damps both ways. If for some reason you want internal mid and treble dampening, you could try gluing your 1” Polyfill to either or both sides of the freely hanging sheets. I don't think it would decrease the flexibility. One sheet with both side covered with Polyfill might Dampen all internal air resonances. Of course, it would not be nearly as effective if the cab is set on it's side or top. You could anchor it at the sides as well, but it would still need to be nearly slack, but not bunching up, and with adequate space on at least one edge for airflow around it, so the air pressure doesn’t rip it off it's anchors. That would be more difficult to do right.
If you are trying to damp cabinet surface resonances, gluing some Quiet Cushion material to the inside surfaces with silicon would probably do that very well, but I'd try without it first – Cab surface resonance is part of the tone. Maybe just try it on the rear surface? That might even be the whole resonance problem there.
