Anyone lined an acoustic piano (on the inside) to quieten it? (and mystery buzz)

[lettersquash]

I'm thinking of lining my upright piano, internally, probably with cloth. The main reason is to lower the sound volume, so as to be less disturbing to others in the house when practising and encourage me to get out of my habit of using the practice pedal almost constantly, which isn't good for my technique. I see a common way to do this is by covering the piano externally, but I don't want to change the looks of it. I'm thinking mainly of the thinner wood panels - above the keyboard and below - but perhaps under the "lid" (the narrow top, I mean, not the "fallboard" over the keys) or other internal spaces. I can't get to the inside of the back, of course, without dismantling it, but another possible location to clad would be on the outside of the back panel. It stands against a wall in the hallway.

So I wondered if anyone's done that, and if they can advise how, or how it worked out (or if anyone would advise not to - I realise, of course, some of these are there as a sound-box, and the tone will be affected). Hence, I'm thinking I don't want anything glued to the wooden panels unless I find a suitable temporary glue, so I can try some cladding and take it off easily if I find it ruins the tone. That might be the only sensible way. Staples wouldn't do, as some of the panels are quite thin, and I suspect the best effect would be if the cloth were held to the wood over most of its area, rather than just fixed around the edges.

There's a secondary reason. It's had a mystery buzz for as long as I can remember. My dad was a mechanical engineer and keen DIY-er, and I remember him spending hours trying to find the source of the trouble, and failing. Now I'm doing the same, pushing this bit, wedging something under that bit, still unable to find the source. Lining it probably won't fix it, but you never know, since I've tried everything else!

[silverwoodpianos]

Purchase a bale of Rockwool and cut panels to fit in the back between the posts. The sound in an upright is pushed against the wall from the back of the instrument. Rockwool has soundproofing qualities along with being fire retardant.
The buzz is probably not related and caused by something loose.