Item 15 appears to be the emulsifier. If it won't come out that is usually because of hard-set gum holding it in. It happens quite often. I suspect that your soaking softened the gum temporarily but did not remove it, and it just set again afterwards. It seems to me that your cleaning work has not been fully effective.
Best next step is to go back to the cleaning, get all the removable parts out, and blast them with carb cleaner under pressure, then blow them dry with compressed air. From your symptoms it is probably getting lean mixture from the main discharge system all the time, but sometimes this is being overcome by the choke not opening properly. The primary culprits are probably the main jet (Item 8) and the emulsifier (Item 15), since the problem is associated with the main system, not the idle system.
