Hi,
I too am the owner of an old Lathe (WW2) similar to a Bantam and as my knowledge and experience grew over the years I had to come to the conclusion I would never get Precision work from it. The cross slide nuts are worn, I don't think the tail-stock has ever truly lined up with the chuck.. Most Lathes have a hollow shaft with a Morse taper (or other) behind the Chuck. This should be more accurate than the chuck if you could get to it and may be able to rig something up if you have access to bits and bobs..
Probably the easiest option is to draw up in 2d on a piece of paper exactly what you want, look under 'Precision Engineers' in Yellow pages and find a smaller firm and just go down there with the Gear and Drawing and do 'puppy dog eyes at them..'
(If you phone them they will put you off.) Say you are a 'CNC Hobbyist' and this may well endear you to them.
This only has a 30% chance of working as they may not have any machines free, but what may take you hours will take them minutes and once you have posed the problem, his engineering brain has already started working on 'How'..
Alternatively, spend 2 grand on a better lathe..