Thanks for the alternate email. Did you find this on edwinjagger.com?
As I said above, you can try gluing something to the broken piece, to give yourself something to hold onto to unscrew it. Or, as Fred D suggested, the eraser on the end of a pencil, might give enough friction to turn it. A guy I used to work with, was a master at getting broken screws out, by chasing the screw around with the tip of a nail.
Unless the screw getting jammed was the cause of the stud snapping, you should be able to get it to unscrew, one way or another. Obviously if the handle was especially tight on the screw when it snapped, it may be a different story.
I'm just curious, do you disassemble the razor and wipe dry, or just wipe dry without any disassembly?
Just going by what I see online, it seems Edwin Jagger razors break this stud fairly often. Mine is about 8 1/2 years old with no problems, thankfully. But I do disassemble and towel dry all of my razors after using them. I know some say that's excessive, but it's just my way of taking care of my tools.
I just reviewed my complete email correspondence with Edwin Jagger back in 2019, and the initial email I sent was addressed to the same [email protected] address that you used. The response and subsequent correspondence was with the [email protected] email address. I would suggest that if you haven't had success with the enquiries email, you might as well try the repairs address. In my initial email I mentioned, and in fact quoted, another post from Badger & Blade recounting the great customer service another person had experienced with Edwin Jagger in dealing with a broken post on a DE89 razor. Maybe that helped encourage the to respond more promptly to my request.Thanks for the alternate email. Did you find this on edwinjagger.com?