Well i can help with some information here.
I asked my girlfriend as she is a dental technician. Her reply was that it would not be an easy fix. Repairing the broken piece would not be something with within a dental tech's powers but a way around it would to be to locate any type of nut with the correct internal size hole and thread and then machine the outer surface down to the correct diameter to fit the inner crown.
The machine work to reduce the nut would not be such a difficult job in itself but identifying a nut with the correct inner thread would be a tough call. Dental tech's have many online suppliers for specialist parts, if somone could name the correct thread dimensions it should be possible to find a match through the industry related websites.

Food for thought.

Cheers - Darren