the one with peg on is a catch plate used specifically for turning between centres – likely will be tight because they are not used often (mine is and needs wringing on with lots of oil!). Should be left as is rather than turned into a chuck backplate.
Suggest you check your spindle for burs flats etc if the catch plate is really getting hung up as opposed to tight – should go on as it looks like Myford type
The Large undrilled one is no good as it has a nose on the front which has the threads
Difficult to see or assess dimensions but if the thread is 1 1/8 in and of correct 12W form, you can clamp it to the face plate and bore out the register in the 'nose; section to 1 1/4 in to fit the lathe spindle to make usable.
I don't know if the backplate in the third picture from top between faceplate and catch plate is the 'large undrilled one' or just the one plate that you say fits.
items bottom right are lathe dogs for use with the catch plate when turning between centres'
the backplate that you say is too big for the chuck actually requires machining to the correct size with the correct register to fit your chuck
If you want another backplate, I would advise a new one from the usual sources rather than a used one (unless you can view and check over yourself). It will come as a threaded blank which you will have to machine to fit you chuck.
Google 'The Amateur's Lathe' by L Sparey on amazon and get a copy – you will find it very useful.
Edited By Martin of Wick on 03/01/2020 09:55:24
Edited By Martin of Wick on 03/01/2020 09:56:14