That wouldn't help I was going to suggest putting a bit of Blu-tac on the rotor arm and, with the contacts lined up, clipping the cap on to get an impression of the gap. It might show the difference up between the two caps.
Some sell a 'spark intensifier' device with an intentional gap - the 'idea' being to allow the HT to 'build up' and then jump the gap -and the smaller plug gap. It doesn't work -as you are finding out. Still your experience is most unusual. Interesting to know if just fitting a better rotor will get it sorted.
When I first installed Accuspark on my Traveller (with 1275cc MG Midget engine), it wouldn't start either. I discovered I had to loosen the distributor base clamp and rotate it by a good few degrees (10-15 or so) then it started and I was able to fine-tune until I got the best running.