The little bit of lathe work can be done with emery cloth using the shoeshine method.
I'll see about a set up to get the barrel out.
OK -- just above the barrel on the inside of the upper are two dimples for the return springs. Cut two rods that will jam between these and the rear of the lower. This will support the sheet metal upper when the upper and lower are together and lets you put pressure on the barrel.
From the inside, the barrel's rearmost ring flushes with the inside of the upper.