My 62' does almost the same thing, in my case it's the clutch/throw-out bearing and all that good stuff. Haven't gotten around to replacing it yet. but I would look there first, maybe search some posts here on replacing the clutch and the other components associated. Could be that there is a worn part that got missed.

also (not sure if its a possibility with a stovebolt) but on other vehicles I have encountered it's easy to install the clutch plate and/or throw-out bearing backwards and it results in similar symptoms on some vehicles.

but looking into clutch parts is alot cheaper than transmissions and all the other parts needed to complete that type of modification.

62' GMC Fleetside 3/4 ton 235 4-speed.
Time makes fools of us all.