Oh one other thing (Rick's post reminded me of it) - I do not segment all the pieces and then drill. Instead, I put the central portion on the tube, turn it until the center part is squared. Next, I take the tube off of the lathe; make sure succeeding pieces/segments are as square as I can possible make them. Then I add the brass and end piece with plenty of CA or epoxy. For me - I make sure that the end pieces are about 1/32 inch longer than the ends of the tubes, I quickly put a clamp on it and bring it up tight/snug and let it set for about an hour.
I have done several this way. It may not be the most convenient way but it is the only way my mind is working.
ON the BRASS: Since I drill the holes first, and if you choose to do it this way - here is a TIP: I place my sheet of brass on a piece of 1/2 plywood that is about an inch larger on each side than the brass sheet. I lay another piece of 3/8 or 1/2 in ply (approximately the same size as the other ply) on top of the brass and screw the two sheets (of ply) together around the edges, with a screw about every 3 inches. Next, I drill holes slowly on the drill press . This will hold the brass and make smooth cuts.
I drill about 20 or 30 holes at a time, space about an inch apart. Then I take the screws out and use some shears to cut out brass "washers". It doesn't have to be perfect, just enough to be a tad larger than the finished blank size. The brass might "curl' as you cut it but that can be flattened out between two boards with a hammer. The holes need to be fairly accurate; the outside does not, as it will be turned down.
I use a fast lathe speed and VERY slow/small cuts on the initial brass portion of the glued up segmented blank.