Thanks all.
I'm just wondering what, in practical terms, accuracy difference we're talking about here, between a coaxial centre finder and an edge finder, and even if it's relevant? By the time I've set the coaxial thing up, I doubt there's much time saving – not that saving a minute (or even an hour) or so is important either way.
I mean, as you can see I faced the stock in the lathe, and found the centre in the mill with the edge finder. It looked spot-on coincident with the machining marks using a pointer in the chuck, so I went ahead and offset it for the throw.
Once it was replaced in the 4 jaw, apart from any cylindricity error in the stock itself, there will be an error in centering the offset, another error turning it, clearance in the eccentric strap, slop in the valve mechanism…etc etc, all of which may add or detract from any edge finder error.
At the end of the day, just how accurate does it need to be for the things I'm building? As I mentioned, the drawings aren't toleranced. I found the suggestion of "just buying the right tool" (at a cost of £60-odd) to be a bit stupid to be honest.