The only thought process for this solve: "Hey, what if I put the arm IN the output?"

Okay. Not really. Locked into using the two arms to make a quicksilver-lead stick fairly quickly, but that meant using 1/18th P. Struggled quite a bit with the assembly but eventually found a nice enough one that ran sufficiently slowly, then decided to see what would happen if I just stuck an arm in the output. It worked. It's dumb. But it works. Further twiddling managed to get the same arm to output the product using just the second half of the tape loop (hence the release/grab in the middle, and arm 3 resetting so it doesn't try to pull the finished product away.)