Just to close this because the problem is now completely solved. Skip to the last paragraph if you don't want to read the process.
I made a mistake in my initial assessment. The lathe was cutting incorrectly but not for the reasons I thought. I purchased a thread pitch gauge and made some more careful measurements and the leadscrew is genuinely imperial which is, I guess, good.
Using some information from this thread I made a giant spreadsheet with all the various gear ratios, and what pitches each setting would create. I then cut a full range of A, B, C, D, E and 1, 2, 3, …. 8. From that I determined that the ratios between each was correct – so A-B halved the pitch, C-D halved, etc. 1-2 made the equivalent ratio of 8-9 but actually did more like 8.5 to 9.5. Based with that information, I was fairly confident there wasn't anything horrifically wrong with the gearbox.
I checked all the gears in the train under the left hand cover and they all matched what they said they should be, despite the lathe behaving as if the 56 tooth gear was actually a 60 tooth gear (if you put 60 teeth in the spreadsheet, the numbers matched the measurements).
I then took the gearbox off, checked all the gears that transferred drive across the gearbox matched, etc. which they did.
Whilst doing that, I noticed that there was a non-original looking spring washer and spacer washer holding the leadscrew drive gear on. For some reason, that gear had been put on backwards and with a very small tweak from the spacing washer it will mesh with the incorrect gear. It, as it turns out, is supposed to mesh with the final gear (gear 8 under the right hand lever) and it had been put together meshing with the penultimate one, gear 7. That threw the overall ratio out slightly, leading to my issues. I've now flipped the gear round (there's a spacer on one side of it), removed the extraneous hardware and it meshes perfectly with the rest of the gearbox and give the correct ratios.
Once again thank you for all the helpful advice, numbers and support. It gave me enough of an understanding to work out the problem and fix it. Now I have a properly working imperial lathe, I just have to metrify it which is much less daunting with everything as standard!