I think all the Chucks I've got are Burnerd Chucks (Winchester).
If you look at your chuck you should find that the screw socket is a seperate plate that the actual chuck bolts to.
Depending what you want to work on a 4 jaw chuck could be better. Harder to set but can be more accurate as you adjust out the wear every time you use it.
Chucks aren't cheap but you might find one 2nd hand. Obviously it's trueness would be an issue. I'm not sure where to get one, have seen occasionally in antiques type places that do tools.
I am surprised the tailstock has no adjustment but i'm used to newer stuff my Lathe is a 1958 Newbie. Usually there was some take up even if it was only on the slides themselves.
Oh final thought, in all the old books I've seen when using tools of that era you must wear shirt and tie and smoke a pipe! Might help
