Hi Andrew, just a suggestion, measure the broken end of the tapered screw.
Find a good bolt of that diameter with enough shank to reach the remainder of the screw in the chuck body.
Cut off the excess shank, place in your lathe chuck/collet and drill the largest through hole without weakening too much the bolt shank.
Providing the hole is big enough to accept a 0.6/1.0 MIG wire or even a 1.6/2.5 welding rod with a bit of insulation on it (the reason for the insulation is to provide positioning ease without premature arcing, probably some very small plastic tubing (windsreen washer pipe)).
If the previous procedure is attainable, insert the insulated welding medium into the hollow bolt and with a gloved hand position onto the broken screw and weld the hollow bolt to it.
I would think the heat shock would hopefully loosen the seized screw.
Hope that may be of help.
Edited By Bernard Wright on 12/04/2020 17:29:54
Edited By Bernard Wright on 12/04/2020 17:32:12