I cleaned and rebuild the carburettor and to my novice eye it looks clean and functional.
Your point about running the bike fully retarded has been noted; I understand it can result in the exhaust valve becoming too hot, hence causing new problems.
I'll share my own experience here. My WM20 has a rebuilt by the REME engine, unused til I fitted it. Good spark, nice clean carb. It didn't want to fire up, and back-fired through the carb a couple of times. Like your bike it did eventually start and ran somewhat poorly for a while before settling in to a nice steady run.
After some frustration I discovered that I was over-tickling the carb, effectively flooding the engine. Now I simply turn on the fuel, don't touch the tickler, set the advance at about 7/8 advance, no choke needed. It usually fires on the first kick.
I was judging this bike by the standards of my other pre-war rides, where flooding the carb usually permits an easy start. This is not always the case!