Use a narrower buttplate (1.5 to 1.6 inches wide or so) and hug the right edge with it. If your cheekpiece thickness still becomes iffy, you can glue and pin a piece of bone, micarta, ebony, antler, etc to a flat tapered face at the cheek piece leading edge and blend it in to give it slightly more width. Good mating glue surfaces are the key. Metal pins can go into an incised line(s) on the cheek piece molding after it is blended in. Not much thickness should be needed. A 3/8” thick strip glued on should be more than enough for a later gun. If you’re still in doubt, I would go with a thicker blank.