My old Super7 tailstock has a bit of play too – but I'm not sure I'd rebore the whole thing and fit a new barrel. At the rate I work – that would take forever!
I'm sure I've seen somewhere (?) that someone with a similar problem simply bored out the front of his tailstock nose for a short distance and then fitted a brass insert that was itself then bored out to fit the original barrel snugly. He said it worked just fine – but I cannot remeber where i saw it – sorry.
So I think that's the route i'll take eventually too but it's somewhere down a long list of Round Tuits…..
Regards,
IanT