I just went through this on my bike, but mine was just one cylinder, i could start it on that cylinder but as soon as i hit the throttle it would die, on mine it ended up being the little plastic thing that went down over the top of the needle (at the bottom of the spring) was getting stuck. i tok it out and messed with it a bunch, swapped it with the one on the good cylinder and for now its fine, I know it will do it again eventually but for now its working.
what i did temporarily last time it happened was used the aerosol seafom and sprayed up into the carb drain and that would dislodge it for a little bit.
Maybe take the carb out and just run that spring up and down and see if the plastic catches.
1992 vn750, 16000 miles
seat shaved , lowered 2 inches in rear, ears shaved, degoated, cpanel is gone just a drag specialties 2.5" speedo
awaiting some pipes