Don't mess up your wood.
You would be the rare guy that a Remington field gun stock would be too high for, Remingtons are known for flat ribs and flat shooting most have to go the other way and build them up to get them to shoot where they look for clays.
You should be able to see all the rib with a slight upward ramp when mounting the gun. Then you never look at it again, only the bird.
If you bury your face that hard on the stock you will start a flinch that will be next to impossible to get rid of.
Get a little coaching from a good shotgun shooter and do a little research on gun fit, WHICH is everything on a shotgun.
Go pattern your shot gun ideally you would like the bird in the center of your pattern (50/50 pattern), the way you are doing it sounds like you would shoot very low making you have to cover the bird with the barrel not ideal for clays, you want to be able to see the bird all the time above the barre/bead and not lose it under your barrel.
Stick with it, loosen up on the stock no future in getting beat up, Good luck.
If you pad or build up your stock as above you will raise your point of impact, back to the patterning board.
Just like ajusting your rear sight on a rifle your eye being the rear sight, make sense?