It only does it once it gets hot?

Look for things that will effect it when it gets hot then! Most likely the plug, coil, HT lead, or cap.

When you swapped the parts to the other bike, did you just run it up and say "yeah, that works... can't be that" and remove them again, or did you actually go out and ride around for 30 mins to check when it was hot?

Heat won't effect the carbs, as it's not like you have an auto-choke, and there's no cold/hot idle system like injection systems that could be playing up. The PGM is well away from anywhere that gets hot, so unless something mechanical (i.e. servo strain) is causing excessive resistance then it's probably not a problem, so you are back to parts that traditionally fail when it all heats up. Coil windings and anything connected to the spark side of things. I've also seen plenty of plugs that look fine when out of the motor and sparking on the engine cases, but fail when under compression/load... even new ones.

If the filter in the tank was at fault, then it's a single line to the carbs. One float bowl will possibly fill faster than the other, but both would starve at a similar rate if the float levels are the same.