So What's the problem when you have the choke off ? How does it react?, Throttle response, Throttle position...
If your down to the 20's it should be more than rich enough. I've once had a carb that needed to be in the low 10's to compensate from clogged pilot circuits.
I've had this same issue with one machine I worked on and the only thing that fixed it was back flushing the pilot circuit. Some crap came out the back way with the pilot jet removed. I did also waste half can of carb cleaner in each carb but that did solve the problem. That machine would work ok but would also lean out just after applying more than 1/4 throttle. After the fix it was perfect.
This is an example of it worked fine and then gradually there was this problem without anything being altered by the user.
So what is yours doing ?
I think by applying choke, you are either effectively lowering pop off to non existant and the pilot circuit is just flowing what ever it can or its allowing the main jet to pull fuel and its using negative pressure (suction) rather than air flow. Once your above 1/3 throttle the main works on flow again.
Also you can get lots of spray from the pilot ports but it takes a while to get the right amount of clean so they flow properly.
And yes I'm in the cleaned carbs multiple times club until I started pouring the cleaner to it excessively!