Thanks for the replies and suggestions.
I tried adjusting the EQ to compensate for the wet towel effect but that was terrible. It sounded so grating on my ears that I had to stop the first song half way through. I didn't even adjust it that much. These speakers really just like it flat. And so do my ears.
Then I moved things around a bit and pulled the speakers out from the wall and it made a noticeable difference with the high frequencies and a little with the depth. It's not the way it was before, but just doing that is a positive change. Before the speakers grilles were maybe four inches in front of the TV but the back of the speakers were around a foot from the wall, maybe a little more. In the new space the TV sits in a bay window with the speakers next to it so the angled parts of the bay are very close to the back of the speakers. And to make it worse, since the bay window is like a giant recess in the wall, the face of the speakers are actually closer to the main part of the wall than would normally be physically possible. On top of that, there are pieces of furniture next to the speakers that sit directly in line with the face of the speakers. Now I have them pulled about two feet out and set slightly wider apart. It looks dumb but sounds better, so they'll stay there for now.
I did used to have a rug on the floor in front of the speakers at the old place. That's in storage now but I intend to put it back.
I have been planning to renovate a larger room down stairs and make that the TV room and move everything down there. That room will have a concrete subfloor with laminate (or maybe tile if I feel like hating myself) instead of a wood subfloor like upstairs where they are now. The walls will still be wood studs but I think the larger space combine with the solid floor will help a lot. I may also do double drywall. It may be six months before all that is done, but I will report back how it sounds when everything is finished.
