Need help for friend who is not going to be around long

Not sure I agree at all. Could be a bad fuel pump or restriction in the fuel system causing poor delivery volume, something in the needle seat/ filter or maybe float level was "set" way too low. If you are carefully "feathering" the throttle I would not suspect acellerator pump. If you are suddenly giving it appreciable "pedal" then maybe so. Not enough pump shot

It's also possible an ignition problem IE not near enough spark power, but if it's as bad as you describe I'm surprised it starts well. So a spark cranking test, test the coil wire and examine the cap/ rotor

A bad cam lobe especially exhaust can also cause popping back through the carb under power.

I SURE hope you can get things rolling for him. I DO agree that in the interest of time and effort, rounding up another carb might be easiest.