If you dont have a way to make the cuts clean and accurately parallel, here is another alternative I've used. Its more labor intensive.
DO NOT slice the blank into segments ahead of time - just drill and cut off the first segment.
Get the first segment glued on and squared as per above.
Use a loose tube and barrel trimmer on one side of the blank to square up that side.
Cut your segment from the blank a little long
Stack the one segment on the starter segment using 5 min epoxy (only one piece, no need for the slow set stuff). Make a sleeve (ahead of time) to go over the tube so you can clamp. Be careful not to glue the sleeve on, but if you do, you can turn it off and make another. Could use CA to speed things up, but I get better glue joints using epoxy, and epoxy works much better on metal.
Once cured, Mount on the lathe and square the new segement.
Repeat until done.
Where you want metal, you can glue the metal and next segement in one step, but note that with 5 min epoxy, its kinda iffy to get more than 2 segments on & clamped before the epoxy gets thick.