I have some experience with smaller (400-450cc) carbureted engines from racing and working on atvs and dirtbikes. They were much more finicky then most carbureted auto engine when it comes to intake, exhaust, and altitude changes requiring carb adjustments and or jetting changes.

Seems to me that problem your having would be more likely to come from a poor fuel supply rather than the carb itself. (partially because the carb is rebuilt) If it were a jetting issue it would run crappy when it was cold and warmed up. I wouldn't expect it to die from an improperly adjusted mixture screw or a choke that didn't function only poor performance. (carbs I have worked on all seemed to fall in the 2 1/4- 2 1/2 turns out on the mixture screw as a starting point)

What has the temperature been where you are during your diagnosis?

I'm not a carb engine expert by any means that was just my long winded way of suggesting you look into the fuel supply and fuel pump.
Have you put a timing light on it?