A conversion could no doubt be done in a manner similar to the Israeli Mauser conversions. Don't have one at hand, but I believe that the receiver ring is cut away to give access to the barrel breech.
How is an M2 Springfield breeched up?
Remington 40X rimfire is 700 based, uses rear lugs, front of the bolt is similar to most .22 bolt action rifles.
I wonder if a P-14 could be converted to rear locking, the barrel face carried further to the rear, and the bolt shortened and its nose reworked with the offset firing pin and .22 extractors. The .303 extractor could become a guide rib. I bet the front end of an existing .22 bolt could be installed on the P-14 bolt body. I think that the easiest way to deal with the barrel would be to use a P-14 barrel breech, and convert it into a sleeve to which the replacement .22 barrel is fitted.
Wouldn't be a low cost project, apart from the barrel work needed, there would have to be a lot of handwork on the action.
Robert - for No. 4 based .22s, there is the C No. 7, and the British No. 7, 8 and 9.