As has been suggested,it would be period to both bolt and single shot older rifles.
There are some resonably priced books by DeHaas on single shot rifles that will show pictures of some of the old custom varmint rifles on single shots.For me,this was rather a blending of technologies of two different eras.My tastes would prefer something like a Malcom scope on an old single shot,but that is just me.The era of putting scopes like yours on falling blocks and such did happen.
If you can find old issues(50's,60's) of American Rifleman,or "The NRA Gunsmith guide",books like "The Modern Gunsmith" by Clyde Baker,and another by Dunlap,Jack O'connor "The Hunting Rifle" you can get a feel for what was "proper" at the time.
Remember,to a degree,rifles like the M-70 and Rem 721 were a response to what gunsmiths and riflemen were developing in small shops utilizing the abundance of military surplus arms available.
It would not be unusual for a scope like that to be used on a sporterized military rifle,often what might be called a "bull gun".
As many springfields and mausers as have been converted,it might work to look around for an old school converted military rifle.Be picky about the metalwork,and you may find a springfield with the bolt bent,etc.
The Rem of the time was a 721/722.Not so common.I think FN Herstal is making M-70's again.If you will search "the montana rifleman" you will discover a source for a clone of the M-70 action.The proprietor also makes barrels,and sells barreled actions.I think the bbl's actions can be had for < $1000 and the actions are in the vicinity of $600.
While you have correctly stated wood would be the most appropriate material for a stock,I think if you look at the design of a McMillan Marksman stock you may see a shape appropriate.(from memory,I may be wrong).
I might not worry too much about the action being drilled and tapped as those scope were typically mounted on blocks on the barrel.
Buffalo Arms specializes in black powder cartridge rifles.The offer something like the old Unertl or Lyman barrel blocks to mount these scopes.
Lastly,there may still be a few crothchety old gunsmiths still alive who used to make such rifles.....
Good luck!!