I'm not a mechanic, but I do a lot of my own work, and the BING carbs are really pretty simple. So......
I don't think it is likely that a needle is "hanging up", (unless you forgot to attache the the "C" clip
) as they are anchored pretty firmly to the piston.
Do a bit of testing to help steer you in the right direction. Get the bike started, and take a short ride to get it warmed up a bit, until it runs as well as it can without choke on. After warm up, stop the motor as soon as possible during or very shortly after the problem shows itself. Most accurate way to get a plug reading is kill motor by letting it run out of fuel while it is mis-behaving. After motor shut off, pull the spark plugs and "read" their color and condition. Wet, grimy black and sooty tip around electrodes and insulators? to much fuel, motor is drowning and running poorly from too rich condition when throttle is opened. Plugs dry and white, motor is starved for fuel from lean condition. Proper mixture should leave plugs dry with a medium grey brown color, not wet or black, not white.
Most frequent contributor to lean/rich problems is improper float setting, or faulty float. Check that first.
Less commoon, needles & needle jets do wear over time, many thousands of miles, as they vibrate against each other, needles tending to get thinner, needle jets get wider, and thus carb runs richer in mid-range. (Needles and needle jets can be changed.)
However, from your description of symtoms, I would suspect and search for a too lean condition during transition from cruising throttle to more power throttle. Too lean during "throttle on" could be from float(s) set at too low, resulting in fuel level in float bowls is at to low a level.
I would also suggest checking the rate of fuel flow through the float needle jet. I once found a bit of rubber from the fuel line upstream float needle, that obsructed full fuel flow, only noticable at sustained high throttle when fuel flow into the float bowl was restricted enough to not keep up with the demand of the motor at high rpm & open throttle.
Or perhaps there are partial obstructions in the emulsion tube(s) that mix fuel and air upstream from the main jet, below the needle jet.
Check for air leaks between carb & motor. Worn throttle shaft "O" ring, bad connector hoses, loose hose clamps, etc, can also cause a lean condition.
I would also take a look at the enrichment circuit (choke) to insure unwanted extra fuel not getting into the motor via a bad gasket, etc, there.
In summary, I think your difficulty is a restriction(s) in the carb fuel flow. Get a carb diagram, Google Bing Agency and get their carb rebuild book, then trace the fuel paths through the carbs understand where obstructions might have occured from foreign matter to residue build up.
Carbs really aren't that complicated. And, like an old mechanic told me once, "they're made from metal, rubber, and plastic. They can't think! If everything is clean and set right, they have to work"
Another smart old buy said "carburetor is a foreign word, that means "don't touch"". At least not until you know that compression, timing, and valve adjustment are all proper, and that the ignition electrical system is working properly.
Finally, don't worry to much about balance, until you have checked/solved the fuel supply problem. If you have completely clean carbs, before you start the motor, be sure that both idle air mixture srews are set about equally about 1/2 to 3/4 turns out from closed. Then make sure the throttle cables have a couple of milimeters free play when pulled up at their brackets on the butterfly valve rod, such and finally make sure the idle speed adjustment is such that both butterfly valves are full closed when the twist grip is completely off throttle.
This should give you a good enough balance setting to get the motor started, then you can further improve the balance by individually and slowly, opening/closing the air mixture screws about 1/8 of a turn at a time, then listening for motor to stablize at best-smoothest idle, repeat for other carb cylinder. When air mixture adjustments are best they can be, tweak each carb's idle speed screw until motor runs smoothly at about 1,000 rpm or so. Small adjustments are best, then wait for motor to stabilize. This should get you a good enough balance to ride to the shop, where they can put the meter on if they have to. More likely they'll just "eye-ball" it, and listen, trying to insure that the carb's butterfly valves both open at the same time, and at the same rate, so that motor not only runs smoothly when idling, but also as throttle calls for carbs to open up. That's all the balancing does. Not exactly rocket science.
Hope this helps. Good Luck! [smiley=thumbsup.gif]
