Looking at your pix on 'small vintage lathes' of the stock being used for this item GB, I did wonder how easy it would be to hold, thread and finish the cap - largely due to this 'up to the shoulder' thing, and the short length of thread required. It certainly isn't easy.
RD's professional advice is clearly the best way to do this, 'inside out', if you have a reversing switch? (Can't remember!)
If you DON'T, would you be able to mount a cranked handle or something onto the outer end of the headstock spindle on an ML4? If you could, I would be tempted to do the threading - in towards the chuck - with very light cuts, turning the thing manually.
You could then at least stop before destroying the workpiece, and also leave the lead-screw engaged while reversing. Repeated cuts at the same setting should allow a reasonable finish if you wind steadily, adjust the compound slide as suggested - and make that narrow rebate adjacent the shoulder first.
A few years ago I had to make a radiator cap for my LE Velocette. (Unpressurised, just a female screw-on job.)
So, a bit of round stock needing an internal thread up a blind hole about an inch and a quarter bore, a bit longer than what we're talking here, but some of the same sorts of issues.
Because I was scared of making a total mess of something I couldn't see very well, I bored a rebate to major thread diameter plus a few thou up at the blind end and cut the thread in light stages by hand, turning the chuck in the usual direction. Could have gone the inside-out route under power as I do have reverse, but time being no object, it worked for me . . . (and as I don't have a dial indicator - something I should have done something about a very long time ago! - I always keep the lead-screw engaged.)
Just a thought, maybe? Only a chunk of ali to lose, after all!