When you set the manual choke, is it pushing the choke valve fully closed? There needs to be a gap between the blade and the bore so some air can be let in.
******
I'm lucky to have a BBS on mine. Hot start or cold, engine runs perfectly. It is a very simple carb. The 1920 Holley seems to be more complex and unreliable.
I was just looking at a 1973 FSM and it flat out says that if there is excessive throttle shaft wear in body then the carb should be replaced. Period. No other discussion.
But the 1968 manual goes into further detail: "During manufacture, the location of the idle transfer port and the spark advance control ports to the throttle valve is carefully established for one particular assembly. If a new shaft should be installed in an old, worn body, it would be very unlikely that the original relationship of the ports to the valve would be obtained." It affects operation between 15 and 30 mph.
Wow, that's enough of a condemnation for me , among others, to start looking for a BBS over the winter. Maybe a 60's vintage. There's been a lot of complaints about how rebuilt parts are a crap shoot these days. Alternators, carbs, starters, etc. FSM's go into great detail about carb adjustments. What are the odds that a mass rebuilder takes the time? Could be a good indoor project for you over the winter though.