You swapped out barrels and the problem persists? Is that correct? I would try a cut down GI stock. They are around and not expensive. I had a very nice M1917 with a 2 groove JA mint barrel. It shot great until it heated up at around 40 rounds. Barrel would then climb and bullets were right off the target. Barrel was likely not stressed relieved by the factory. I sold it off for a profit. Sometimes you just move on.
I missed that part too! Now that increases the number of possibilities. Could be the receiver is not trued up or the installer bent the barrels on installation, stock warped, etc., etc. etc... Without pics this thread is like pi**ing into the wind.