More complicated than needed, Just hook up a restriction tube and transposer to feed back into the top of the barrels. The restriction tube makes it a last priority path, the transposer makes it one-way. Anything that "overflows" will just go back up into the main system and go back into the barrels (or whatever other overflow you have in case the barrels are full), while the transposer keeps anything from the main system from entering the closed manager system. The real problem with this is the sheer number of managers needed, one for each barrel.The problem I foresee with your last idea is what happens to the surplus that is pulled out of the barrels by the managers? Once your destination inventory has its 64 of 'whatever' it will send the rest of the items coming down the pipe back where they came from. That works great for a chest but barrels don't let you insert more than 1 stack in the bottom. The best solution I can come up with off the top of my head is to put a restriction tube underneath the barrel and then connect an ender chest or item tesseract at 90 degrees so that the backflow goes in there which is then sent back to the start of your barrel sorting system to be restored. However I'm not sure how managers react if there's a restriction tube in the way as I've not tested it.