Those old scopes were free-recoiling. They slid forward with every shot. Then you pulled (slid) them back into place before taking the next shot.
(You need to Login to view media files and links)Steve Earl just listed a mount very much like this for the 1903 Springfield for use with a Leatherwood scope. AFAIK, that's a Chinese-made reproduction of a scope very much like the one pictured.
The more common types of externally-adjusting target scopes (Lyman, Unertl, Fecker, etc.) attached to mounts that were more or less interchangeable. The Winchester A5 and its Lyman variant and the recent MVA B5 do not fit the standard, but are much smaller. The old scopes usually sell for $450 (for a beat up Lyman) to $650 or $700 for a pretty good Unertl. The smaller Winchester types bring the same prices but are pretty flimsy, not a good investment IMHO.
Steve will make custom mounts of almost any description. Those of us interested in such things might want to consider a group order. My guess is that the mount & screws will cost about $150.
Steve Earle also advertises that he will reproduce old screws in small batches.