I got this tip from a serious custom stock guy named (fnu)
Atkinson and it worked great on my high gloss Rem 700s, now
replaced by Rugers. No Booos!

Get some rotten stone from the hardware store and a fine
plastic sanding pad. Mix the rotten stone into a slurry/paste
with lynseed oil and use the pad to lightly rub it over the stock.
It comes out with a subdued satin finish and no scratches. If
you handle the rifle a lot, the burnishing will bring up the shne
again but it is simple to knock the glare back down with
the same preparation. It also lets the wood character come
through.

Good luck,
1B