I bought a Savage Westpoint 842E (same as the 340) and it had a Savage Scope already on it. From the looks of it I would say the scope and mount were installed by a smith or the original owner not the factory. Because the mount is attached to the side of the receiver I would suggest it be installed by a gunsmith and an experienced on at that. If you have a strong background as a machinist you might give it a try. I can say that my rifle is dead on at 100 yrds with the 4x32 scope. I have seen the mounts and also matched scopes on Midway USA and Numrich Gun Parts web sites. The mount does not allow for more than approx. 1 inch fore and aft movement of the scope. If you decied on a scope I would suggest meeting with a gunsmith and have him measure the placement of the mount/scope to match your body build for proper and comfortable eye relief.
Everything I have seen on the peep sights suggest that they fit into the tapped areas you mentioned. The problem with a peep sight might be in finding a set made for a rifle that has been out of production for so many years.
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