Hi BigJim, I'm following this post intently as I've had the same experience on my '54 Golden Flash. It will run all day perfectly at 55 mph, but as soon as I push it up to 60-65, within about 30-60 seconds I'll notice a miss, which will quickly grow to a cough and finally it backfires. However when I pull over it idles perfectly and I can immediately ride away as long as I don't go over 55 (slower speeds if in a lower gear so I think it's around 3700-4000 rpm). I've filled the petrol tank and drained it into another and it flows perfectly, no tank vacuum, fuel is getting to the 276 carb, checked tappet clearances, timing is spot on. Ran it in the dark to check for any visible electrical arcing.
I changed the carb to a 375 monobloc and no change. I have run the bike for about 8 years like this, as 55 mph is just fine for me, but something is obviously wrong. I have always noticed that if I applied the choke it would delay the symptoms for a while. So just recently I played with the mixture settings firstly installing a larger main jet, then I raised the needle 1 notch at a time until I ran out of notches and "voila" it didn't miss at all. I ran for about 10 miles at about 70 mph and it ran fine, however when I got home I pulled the plugs (L82C) and they were very sooty, so continuing to ride at those settings would certainly foul the plugs eventually.
A friend of mine who'd I term as an expert of British twins believes it's probably the magneto is not able to create enough juice to fire the plugs at high speed, and richening the mixture aids in the ability to fire at speed. I did have the mag rebuilt a few years back, but I supposed it could be that, I tried every thing else, I think.