The Keystone stocks are indeed fat and you do have room to thin them up to an SA C stock profile. Where you will need to take a close look at is the area behind the lower band. If you have enough there to take out the checkering without making the band prouder you can probably do it. I expect you'll have to thin up the hand guard as well. The wrist area shouldn't be a problem. Notice the stock cross bolts and how much they are recessed, you will have to thin the stock the full length, not just where the checkering is. Again, plenty of room to thin there.
Good luck and nice looking gun.
Kurt
As the late Turner Kirkland was fond of saying, "If you want good oats, you have to pay the price. If you'll take oats that have already been through the horse, those come cheaper."