Thanks all for the suggestions.
Mandrel. Why on earth I didn't think of that myself I do not know. Perhaps my brain goes open-circuit at times! What's more, as Colin says, it would achieve that concentricity between both ends which, given what I have already done, I can't now guarantee, not without scrapping the work and starting again.
Boring tool. Thought of this one, but scrapped it because I hadn't thought about reversing the lathe. In any case, without major re-working of my cross-slide and tool posts, I can't get the cross-slide far enough over to be able to get the tool down the far side of the work.
Left hand tool. I tried this with a high carbon steel home-made tool. It did work after a fashion, but the resultant surface was not very good which suggests that probably my angles & cutting point were wrong, yet it would seem that I was indeed on the right lines. As it happens, I don't have a SCLCL tool, or indeed any other suitable left hand knife type tool so couldn't try it, but it does seem from Jason & Chris to be a goer so I will shortly be looking for a suitable tool for future use.
But in the meantime, here's what I've decided to do. First, I must point out that although working for the best precision I can achieve is always desirable, the actual end result is nothing more than a handle with an adjustable graduation collar hence a slight loss of concentricity probably doesn't matter. Therefore I have decided to transfer to the 80mm 4-jaw chuck since I can hold the work on the outer step of the reversed jaws and hence do the necessary two-stage turning and then the boring.
Now, why didn't I use the 80mm chuck to start with? Well, I was hung up on holding the work with as much jaw as I could get onto the work, and since the 80mm with the jaws in standard position wouldn't hold the work, I decided to use the 160mm chuck, and hence the problem as outlined above. Had I thought to reverse the 80mm jaws and accepted the slight loss of grip, then the problem would not have arisen. A case, I think, of not thinking the job through thoroughly coupled with a lack of experience.
Anyway, thanks to all,
Peter G. Shaw