just a quick thought,I recently had to drain my tank,(CB500-4) the fuel tap did a similar thing,full flow from one outlet,dribble from the other,this made me think,a very rare occorance !
is the fuel taking the line of least resistance?
in normal use,it fills each pair of carbs,guessing the full flow fills faster,when that is full it means the only out of the tank is by the "slow"
pipe ?
as both sets of carbs will normally use the same amount of fuel,it is likely to happen after maybe a dry start ,were the carbs are empty,
or if it runs onto reserve,
this is not a sure cure,but something to ponder on,
try putting your finger to stop the flow,and see if it increases in the other pipe,