Now that I've gone through the process of removing and working on the carbs for the first time... holy crap! Look at those handy little Allen-head screws on the bottom of the carbs for draining the float bowls. Might actually be easy. And I wouldn't be in this predicament if I bothered to learn that before.Makes too much sense, can't possibly work.
Yup, I made sure I cleaned them as part of the rebuild. Nicely unblocked.