Sound carpet

I'm in the process of convincing She Who Must Be Obeyed to do that with a small mobile shag carpet that was found to resolve the sound issue and will be stored away when I'm not listening to music ...
In parallel, I'm also looking for a permanent solution under the thin carpet ...

In parallel, I'm also looking for a permanent solution under the thin carpet ...

not sure how you plan on putting something under the carpet as you would have to pull up the carpet and pad from the tack strip and then have to re-kick the carpet so its tight again.

Grow a pair and tell her this is a must.

Area rug. Possibly treat reflection points at side walls, too.

Assuming this is a new area rug and not wall to wall, I would find a piece of foam carpet pad at the big box stores. Have it cut to size just smaller than the new rug by  a few inches, and place it underneath. The extra padding could help.  And it won’t cost you much to give it a try.