I had a 340 in .30-30 that was made in the early 50's, before they drilled and tapped it for the scope mount. It had the really neat Dockendorfer rear sight with the elevation wheel. I also had a Savage peep sight that I mounted on it. It was a good shooter, about 1-1/2" 100 yard groups. So what did I do? I got rid of it, of course!
I also had a later .222 that would shoot 1". The problem I had was with the tiny brass extractor. Even replacing it didn't help. That one was sold also, but I don't miss it like I do the .30-30. A local gun shop has a 340 and also the Stevens equivalent with the spoon bolt handle. After he has had them for a while, I'll try to talk him down on the Savage.