Just pull the carbs and disassemble 'em one at a time and thoroughly clean them. Strip the carb body down to parade rest and dunk it in the good carb cleaner gallon cans - about $35 from auto parts stores. Used compressed air to verify EVERY fuel and air passage. Follow the fuel and air passages by looking at the casting bumps - you can tell where the passages go from/to.
Replace any O-rings. Inspect the diaphragms, but they'll probably be OK. Be very gentle with them. Make new gaskets for between carb & manifold and manifold & head, or get new O-rings, if that's what they have.
When you assemble all four of 'em back together as a unit, bench sync them before you put them back on the bike. One carb is the 'master' and the other three sync to it. Set the master so the butterfly just touches a 1/16" drill bit sliding thru. Then, set the other three carbs to do the same to the drill bit. That will get you very close to be going on with.
It's kinda fussy work, but it's not at all difficult, but there really are no shortcuts to eliminating these kinds of carb problems. Just go ahead and do it - you'll be miles ahead of just trying the piecemeal, hit-or-miss approach.
Great bikes, by the way. I had one way back when, and loved it. It's one of the very few of the 50 or so bikes I've owned that I wouldn't mind having back again.
And, if you haven't already done so, check out the GSResources page. Great help and knowledge there for all things GS.
http://www.thegsresources.com/Good luck, and post some pictures of your new ride, if you get the chance.
Kirk