JIm, Your problem sounds to me very much like the distributor. I have messed around with flathead distributors quite a bit and the one thing I can tell you is that they are generally a pain in the a**. The worst style is the earliest being the diver's helmet used from 1937 to 41. Of course, this is the style utilized on the UC. The main problem I have encountered is usually the coil mounted on top tends to overheat and breakdown dropping the output voltage to less than ideal. To give you an idea, early coils were lucky to put out much more than I'd say 15,000 volts. Upon thermal breakdown you lose adequate voltage failing to ensure proper firing. Another possibility is that the centrifugal advance weights are stuck, lose or old, the timing cycle bad etc. By the way, any books that suggest a method of setting the timing eg. a carrier manual, by hand are garbage. The only answer is to find someone with the proper fixture for setting flathead distributors.
Trust me, I've seen this so many times it's not funny, but everyone has an opinion as to the miracle cure, NO it couldn't possibly be the dist. or something like that. Good Luck!