So having to have the choke all the way out is richening it up which means at no choke it is way too lean. This could be from slow speed needle adjustment being too lean, or clogged idle passages or a combo of both. It could also mean you have an air leak at the gasket for the carb/manifold connection. It could also mean you have a sticking needle valve or faulty fuel pump and your carb bowl is not filling up, but if this were the case it would not run well at high speed which you didn't mention was a problem.
Have you tried messing with the slow speed needle adjustment any? As long as you note its current position you can toy with it and return it back no problem. I'd start it at 1 & 1/2 turns out from lightly seated and then back it off 1/8 turn at a time with 10 second pauses between adjustments. If you get to 3 turns out and no noticeable change then I would revisit the carb. Sometimes after a cleaning debris can still be washed in from the fuel tank or fuel lines and clog the slow speed passages even if you cleaned the carb perfect. The only way to tell is to pull it apart again though.