Agreed...Replace parts with known good parts..... Some times it is super hard to try and diagnose the issue exactly. Some times it is easier to just replace the serviceable parts with known good parts. If that doesn't fix your issue, then I'd say it is probably one of the major components in your engine. Without seeing it, I couldn't really, with any sort of certainty, properly diagnose your problem. Best thing is to list out the serviceable parts and mark them off as you test/replace them.
One other thing to kindof re-enforce what others have said. Just think of it this way. When you have your choke on, you are feeding the engine more fuel than air. So when you have your choke off in the flat, horizontal position, you have a more even F/A mixture, or at least you should. If your engine doesn't run when the choke is OFF, and runs with the choke ON or partially ON, you are presenting your engine with a lean condition (as in, not enough fuel, and too much air). Your low speed needle needs to be reset to the 1 1/4 turn or whatever the default needle settings are for your particular carb. Also, reset your high speed needle to the factory settings as well. Small adjustments (1/16 of a turn) make HUGE differences with these engines. Large turns are not beneficial.
From my experience, this is what has worked for me, and continues to work for me. Proper break in techniques, and patience when tuning the carb allows you to keep your engine running for a long time.
One last thing, what type of air filter do you use? Do you oil it? Have you cleaned it lately? Soap, water and let air dry.
Just some ideas to consider.