If adjusting the choke doesn't help, try adjusting the choke pull-off. It may be opening up the choke flap to an angle that it just doesn't like on a dead cold engine.
If the choke and choke pull-off adjustments don't correct the problem, take the carb apart and replace all the internals with one of our SR kits. This will get the carb up to par for modern fuel, and give you a chance to check out the power piston, and everything else inside to make sure things are clean, correctly adjusted, and working like they are supposed to.....Cliff