As Koan said, the air filter did badly affect higher rpm and also to some extent the mid range. Seeing as the carb is all standard, I can only assume BSA fitted a very free flowing filter as standard. I have removed the filter and she now revs cleanly right up to high rpm.
The 30 pilot jet had a similar affect to the air filter. I know the carb tuning charts show that the pilot jet has zero effect on wide open throttle, but I have to disagree strongly with that. I have messed around with pilot jets on several Bantams and they always have an effect on every part of the rpm range. The 30 pilot today had quite a significant effect at wide open throttle. It would not rev out, (felt like a rev limiter) and actually started to bog down. I replaced the pilot with the standard 25 and now she revs cleanly again.
With the air filter and/or the 30 pilot fitted the cough and stall was improved a little, but as I've said above, the rest of the bike was ruined.
So it looks as though whatever I do to alleviate the cough and stall, problems turn up elsewhere. I'm sure in the hands of a better carb tuner than me, this could be sorted, but for now I'm just going to live with it.
I've been talking to a guy that knows a good bit about tuning racing Bantams and C15s for trials, and he has advised that I should get that scoured inlet port sorted
(back to standard) before trying anything else. So I'm going to use the bike for this season as it is and get the head and barrel off in the winter to try and sort it. I will revive this thread if I ever make any progress, but for now I'm afraid I'm done. My brain can't take anymore.
Thank-you to all that have taken the time to help. Much appreciated.