340 has me stumped

Allow me to throw in my .02 on this.. Do you know if the heads have had hardened seats installed? Are you using any fuel additive to compensate for the loss of the lubricating lead that used to be in the fuel? The problem you describe parallels the issues I have had with my 1969 Toyota Corona. The car would start/run/idle fine for the first 20-30 minutes of driving, then quietly develop a serious miss/stumble when returning to idle. Being a pushrod 4 banger of low compression,, this issue couldn't hide among the other 4 jugs like your engine can. I would pull up to a stop, pop the hood and start pulling plug wires... sure enough,,there would be a dead jug.. problem was,,, the dead jug wouldn't always be the same the next time it acted up. Sometimes, the idle smoothed out before I could start pulling plug wires. I deducted that to the valve and seat cooling enough at idle to cure itself. I took off the head, lapped the valves, reinstalled, set clearance ,,, Ran flawlessly and the problem went away for about 1,200-1500 miles.,, Slowly the symptoms would return, the car would never stall,,,but stumble and miss more frequently as miles added up. Please let us know what you find out.