At this point I would try and clean up those spindle threads with a triangular file as previously mentioned, you really have nothing to loose. There is quite a bit of thread before that, so I feel there is plenty of strength left. I also need to say this next thing, and that is a file may not actually work for that as that spindle should be a hardened piece and will be very difficult to file for anything more than small burrs. You may have to actually grind that away with a Dremel and their thin wheels.
Regardless of how you fix it, the piece should screw on without resistance till it contacts the spindle face. If yours doesn't after attempting to fix, it either needs more fixing, or you have also damaged the threads on your accessories also.
As was mentioned, some lathes with their corresponding chuck thread inserts, oneway I think, will work with screwing the set screws down as the spindle has a groove for that. oneway does this because of their outboard attachment. If not turning on an outboard spindle, you should never need to use set screws.