Can we talk about this "thread broke off while drilling hole"?
First, which hole? (I'm guessing the one through the threaded tenon where the ink cartridge/converter goes, but you might mean the one through the grip section where the nib unit will go.) What diameter are you drilling out?
What diameter do you make the tenon ready for threading? And what thread specs?
Not that there is only one right sequence for the steps to make a section, but it looks like you're leaving the risky operation till last, when you've done a lot of work and therefore have a lot invested in the part.
I do things in a sequence that (after the blank is a straight-sided cylinder) puts the tenon threading first, then drilling through the tenon, then parting it off the ebonite rod, flipping it around and drilling the steps for the housing and threading for the housing. It gets the risky stuff out of the way before I spend any time shaping and polishing the section, so I don't feel quite so bad when the tenon snaps off. (Notice I say "when" not "if" - I've made a lot of sections and it still happens to me from time to time.)
FYI - typically I make the tenon 8.9mm diameter with a small chamfer on the end, and thread it M9 x 0.75. I do not cut away threads at the base where the tenon meets the body of the section, it is safer to remove the first couple of threads from inside the barrel. Then I fit a threaded collar (helps keep it from exploding) and drill it 0.25" or slightly larger for the ink cartridge/converter.
Hope this helps -
Duncan