If you can chamber a 30-06 case in it,,load one up w/ 3 or 4 gr or Bullseye. Stuff the rest of the case with cereal or a wad of TP. Fire form it in the chamber and see what it measures out at.
This still won't indicate any excess chambering length, but a misplaced shoulder on the fireformed case will point you in that direction. Then it's time for a chamber cast.

Try gripping & turning the long screw out. Perhaps the sheared off one can be gotten to turn with some careful chisel work.
If they're both 6-48's,,personally I'd just clear them and re-tap to 8-40 if you're going to re-scope the rifle.
If one is a broken tap, heat it with a tiny O tip flame to anneal it first. Isn't going to hurt anything on the rear deck where it is.

Plug all the holes to hide them if going for classic iron sights, then you can reshape the wood to elliminate the MC.