Sound 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. 

Meet her in the middle with a rug that's halfway as thick as your shag carpet and twice as thick as her thin one. If all it took was going down in thickness then coming back up some should do the trick.

All the best,
Nonoise