Very neat rifle. I'd just give it some TLC and maybe stabilize that crack, and leave it as is. Although, I would really have to fight the urge to break out the checkering tools and checker that stock. Maybe copy an old Wundhammer pattern.
My first thought was NRA sporter, but the lack of crossbolts and the cheek piece rule that out. Possibly the barreled action wore a sporter barrel when it was first stocked, and was later rebarreled with an issue barrel which is a lighter contour. I have an NRA sporter that was reworked by G&H. In order to improve the barrel inletting, they turned a wood dowel to fit the barrel channel, glued it in, then re-inlet the barrel into the new wood. Anything is possible.
John