Another rebuilder is
http://quadrajetpower.com/ out of Texas. They rebuilt mine, including re-bushing of the throttle shafts and I was happy with the result.
Lots of great advice in this thread, the biggest thing is to just keep at it. It sounds like several variables are in play and methodically working your way through them is the best approach. I agree with others that solving the flooding issue is priority 1.
If you have the time to dive into it--and to be methodical doing it--do what someone else suggested and remove your carb to the bench and check it out. Lots of good material out there on rebuilding to get you through the assembly, including the very important but often overlooked tip about how the needle hangs on the float.
IMO the Qjet isn't complicated but it is nuanced, patience and understanding of its systems will go a long way.