What an interesting thread is this! I have been to somewhere quite close to this place myself very recently. BTW I call the thing that fits on the taper the clutch sleeve and the inner part of the clutch that fits on it I call the clutch centre.
I feel that Brian (reply number 18) has hit the nail on the head with your problem kiwipom. The photos do suggest that the clutch sleeve is sitting too far out.
BSA used the same tapper on every box ( that had one ) it ever made and these include ones for cars, stationary engines ( reduction & right angle drive boxes), invalid chairs , farm equipment ,,,, the list goes on.
They all look very similar but they differ in the size of the hole.
As it is a tapper, the bigger the hole, the closer it sits to the gear box.
AFAIK there are 4 commonly used on bikes, 2 long ( for big clutches ) & 2 short ( for small clutches ), one with a big hole for tin primaries and one with a slightly smaller hole for alloy primaries. The difference in hole size has the clutch sitting between 1/2" & 1/4" out of alignment.
Oddly enough there only seems to be big & small listed in the parts books but I have a box of them dating from the early days when I did not know any better and shoved all of the sleeves from all of the clutchs together in an oily box for storeage.
It took weeks to find the correct combination of sleeve & center to replace the single spring clutch for a 6 spring on the M20