I'm sure Monte knows the proper saying, but on airheads if you think it's electrical, check the carbs, if you think its the carbs, check the electrics.
To let fuel out of the bottom of the tank, you need to let air in the top. The gas cap on the R65 holds this vent. Try riding around the block, and when the bike starts to bog down, unscrew the gas cap. If it is able to rev again, that would indicate a clogged tank vent, which can probably be shot through with solvent and compressed air.
If you balanced the carbs without taking the bike out for at least a 10 mile ride, they will probably need balancing again. The bike needs to be fully warmed up. It should still run, it just might be a little rough or have a high idle when warmed up
I can't stress enough that you should read the plugs, it is a very easy way to help determine if the carbs are parched or drowning.
A few other carb things:
-if you took the needles out of the slides, you need to make sure that they are set in the proper position. They are adjustable and will substantially affect the mixture on the main jet.
-make sure that your choke cables have slack and that the choke levers on the carbs are fully returning.
-make sure you have no air leaks around the carb boots.