With respect to making octagon to round barrels...
Years ago I machined a quantity of barrels on a 16" South Bend.
Tapers were turned by offsetting the tail center.
I milled the flats as follows...
Took a piece of channel iron. Made and mounted a couple of V-blocks, one at each end. Took a piece of octagon barrel, turned a portion of it round, to just slide into the barrel bores. Drilled out the bore of this piece, and threaded the octagonal end. Bored a taper in the round end. Machined a piece with an enlarged taper on one end, matching the internal taper of the piece that fit the barrel and the other end threaded to screw into the octagonal end of the barrel insert. Slit the round end. The result was an expanding internal collet. Slip it into a barrel, turn the inner piece, and the round end would expand to grip the barrel firmly. The protruding octagon portion would engage one of the V-blocks, indexing the barrel, the round part of the barrel would rest in the other V-block. The barrel would be clamped in place.
The assembly replaced the lathe compound. It would be set at a slight angle to the spindle axis of the lathe. An end mill was held in the chuck. Power cross feed was used to pass the barrel across the end mill, the carriage being locked in place. When one flat was milled, the barrel was rotated 1/8th, and another flat machined. Keep going until all 8 flats were cut. This rig worked very well, didn't take long to mill the tapered octagon section of the barrels.