I've just read thru this whole thread and one thing that I don't recall being mentioned is that BLACK/HOT wire goes to the GOLD/BRASS colored screw and the WHITE/NEUTRAL wire goes to the WHITE/NICKEL PLATED colored screw. The GFCI won't work if that is not followed.
You may have hooked it up in...
The real question is how much you want to spend to repair it? If you could find a plain spline hub or coupling that matched the spline shaft, a bit of machining might get a replacement insert that could be brazed in place. This assumes the hollow shaft where the old spline was is steel and not...