Likely the blade tip is touching the bottom of the slot. Grind the driver slightly on a sharpening stone keeping it vertical until it does not cam out anymore.There are are drivers with a torque knob which are useful for bracelets. And to be on the safe side heat the part with a lighter to loosen any locking agent that may be there.
I ended up taking the barrel and ratchet-wheel screw from the "parts movement" that you found on eBay. I also purchased that NOS 1790, but the movements in these watches are the larger 1692. Still gives me a complete unused movement for parts.
Attaching some images - not sure how this is going to be formatted in the post (perhaps should have inserted using links).
But in the order that I think they will be in:
1) The newer movement fully serviced with the new barrel and ratchet-wheel screw.
2) A look at the dial before remounting in to the case.
3) Look from the rear - all mounted with the back off.
4) From the rear - with the back on.
5) The parts removed (barrel assembly complete with broken off screw head).
6) The two watches side by side.
7) My great uncle's watch from the rear with the original strap mounted (this strap came on the one I just acquired).
8) My great uncle's watch from the top in the correct original box (also came with the watch I recently acquired).