Sound diffusion panels--do they reduce brightness?

Two other issues are the equipment and the recordings. You didn't mention the make and model of speakers or the other equipment involved. The reality is the current fashion for a lot of audiophile gear is to sound bright. That's not meant to imply everything out there is bright, but the odds are not unfavorable.

I imagine you intentionally chose the gear you have now so I presume it sounded correct to you at some prior point. You might want to compare that previous environment to the one you're in now.

Recordings are also often bright. Close miking and the generous use of EQ and other effects are very common. Even classical recordings are not immune to this issue. Does your brightness problem occur with all recordings or just some?

The tonal balance of my system is just where I like it on an overall basis, but my biggest frustration these days is the variability in recordings. It never ceases to amaze me how many releases are poor and artificial sounding.

Keep in mind the point of listening to music is enjoyment. For most of us, it should not be an exercise in deprivation. Leave the self-flagellation to those working on the fast track to sainthood.

What can be useful is to simply experiment a bit. A few inches this way or that, or the addition of a throw or other covering may offer the improvement you want without major decorating surgery.