350 hp out of a fairly stock 340

That was done for insurance purposes and because if the buying public knew how close it was to the 383s, there wouldn't have been as much market for a 383.
Flame on!
There was one more reason VERY close to your 383 comment. 1968 was the first year for the 340 AND the Road Runner. They did not want people to know that you would get a 335 HP V8 in a road Runner, and that it was ONLY 15 HP more than the 340. Plus, an A Body with a 340 can beat a 383 Road Runner every time.