Thanks for all the advice.
I'm stalled at the moment as the press I made turns out to be too small so I'm re-working it to have the full height needed. A lesson in drawing things out before getting out the angle grinder – especially when you a novice like me.
Just to note that the spindle with the marks is the old one. The marks seem largely due to the bearing coming off in jerks.
My plan now (when I've finished the press rework) is to push on the front bearing and then try and trial fit the back one with some light oil.
If it fits smoothly, I'm a happy bunny. Nothing indicates that this will be the case. Depending how how well it does or does not fit, I will either try and blue up the shaft and scrap or try and reduce a little. I have a small 4 jaw chuck which fits my mill and as long as I don't do anything heavy I can use that to polish the shaft down a bit.
I'm minded to think, at the moment that the shaft is just too big but round.
I will keep you posted.
Iain