When I finally got a chance to look more closely at the broken pin, I could see just the slightest remnants of threads on the broken end. Then, looking and poking at what was left inside the hole, my suspicion was confirmed when the piece inside the hole rotated a little bit.
Unfortunately, it only rotated further in, I couldn't get it to unscrew. I drilled a small hole in the middle of the piece and was able to jam a jewelers screwdriver in the hole, but could not for the life of me get it to unscrew. It would only go deeper into the hole.
A couple of hours of trying this and that, and I have given up. The only hope I have now is that the round, half-inch diameter piece that in turn had the threaded hole for the spool pin is a press fit in the machine body, and can be popped out from the inside, through the access hole on the back of the machine. It's a difficult angle, but maybe it will work. And, maybe I can get the stub of the spool pin out then.
In any case, I'm now mentally prepared that this will likely become a parts machine.
Thanks, anyway.