The sputtering/popping out the carbs is a lean condition. But, the idle, if it had a constant vacuum leak(still to be detirmined) would be bouncing a little more regularly. Start the bike. Get it idling without choke. Have a can of carb cleaner with a straw. Sparingly spray around intake boots/manifolds. Careful that over spray isn’t going in the air intake or the test will give false positives. If the bike dies or idle drops considerably, you’ve found a leak. (Do not use water to find leaks). The idle bouncing every ten to 15 seconds is a symptom of inconsistent float level or fuel restrictions. But you’re gonna need fresh fuel as high octane as you can get from the pump. 91/92 octane. No boosters. A couple gallons in a clean can. You’ll feed your bottle from this. A few pints at a time. Not sure if the bike has a vacuum actuated fuel petcock either. But until consistent flow can be determined we’ll keep the variables to a minimum. Also fresh spark plugs, a recent valve adjustment, and the integrity of the ignition components should be verified. A compression test couldn’t hurt either. Maybe good time to inspect gas tank and petcock for debris and functionality.
Anyway, you don’t have to throw money at it to diagnose. I wouldn’t recommend removing carb manifolds until you know they’re an issue. Bikes of this era start disintegration on disassembly. Diagnostics are how we determine what needs repair. Plug vacuum leaks (with duct tape if need be) while you search for more. Throwing parts at projects until issues are resolved, we’ll reserve for factory backed service departments.
Im concerned that you said “bench balanced” and “rebuilt” carbs. By “rebuilt”, “I’d” mean replaced all gaskets, orings, seats/needles, set float heights to spec, snaked out all circuits, and bench tested for fuel leaks and air tested slide speed???? Since Idk what has been performed I’ll start with fuel. You’ll have to have for fashion an I.v. Bottle for the balancing that has to take place on the bike. Make or purchase a manometer as well. Take the tank off and air filters. Make sure area undertank and above/around carbs is reasonably clean from dust, dirt, debris, and hardware. We don’t want garbage sucked into the engine. If you leave your project for any amount of time cover the carb intakes. I duct tape mine like I’m gagging a victim. (Rag in the mouth tape over rag)
Once you have eliminated the variables and your manometer and fuel bottle are set up you can balance your carbs. Do not attempt to set the fuel/air ratio (beyond what’s needed to keep from overheating during balancing). Once your carbs are balanced, replace the tank, air filters, and hoses. Carful that the tank position doesn’t pinch or ground anything out. Take the bike for a spin to get it good and warmed up. Then set you air fuel ratio. Keep in mind as the weather gets cooler ratio’s need fine tuning. A change of more than ten degrees before even thinking about it.