By any chance, has it been converted to a fuel pump system? If so, how was it done?

Back to basics, it needs fuel in the correct amount, spark at the right time, compression, and what many forget, crankcase compression. Your problem is in one of those areas. Sounds like you have covered most of them. Without any reason in particular, I am thinking crankcase compression. Checking the reeds was wise, but non-productive. Piston rings provide compression, but trashed piston skirts can affect crankcase compression. Has it ever been overheated?

Thinking deeper,, is it getting water into that missing cylinder?

Pulling the exhaust cover is a lot of messy work, especially on only a “hunch”. Water droplets should be fairly evident on the plug if water intrusion is an issue. You mentioned that you “swapped the reed valves”, just how did you do that? It is kind of risky disassembling the reed plate and swapping the pedals around, flipping them around can cause them to break.
Tell us more about this engine, you mention it has always been a strong runner”…Tell us when it last ran properly, and what work was done that might have affected it… You seem confident that the engine is actually sparking on both cylinders, how have you confirmed this? Just cuz it is sparking on both while cranking, doesn’t mean it is sparking on both while running. You might try those inline neon testers to make sure it is actually sparking on both while running.
Will it run on two cylinders at any speed? In other words, will it run on both cylinders at high speed, but loses one at low speed, or perhaps vica versa?
Crankcase leaks/primary compression could be an issue, but something would have to be radically wrong inside to keep the engine from running on both cylinders at high speed. Keep in mind that primary compression issues might not affect compression gage readings at all. A good example might be a broken piston skirt….Something like this just doesn’t seem very likely on this brute of an engine.