You really only have to go so far as to clean those parts and leave the floats alone. No fuel leaked out. The other carbs run and do not leak. You found the problem. Think spark-fuel-compression.

You have the long skinny jet is the idle and slow speed. The smaller jet with the needle you mentioned is the main jet. If you pull that main jet out and it screws out with the emulsion tube, all the better. If just the jet, then make sure it and the low jet have daylight through them. Reinstall and do not over tighten the low speed. Better you think it's tight and let it fall out, rather than you hear it shred, stretch and snap that tiny thread off.

But you sound competent enough to get the carbs off and to the bowl... Touch nothing else because think about how the bowls do not leak and what is not needed. Do not open a can of worms. You nailed the diagnostics. So the less work, the better. Good going!