You could be chasing the wrong problem. Backfires in the exhaust are useualy a secondary ignition problem. Unless you have raw fuel dumping down the carb when ideling or accelerating. That you would see. If it were somthing plugged it would probably backfire through the intake. When was the last set of cap & rotor, plugs or wires installed?
It sounds like you are loosing more than one cylinder so the cap and rotor are where I would start. Plugs are a must if your carb was the problem. If you have an ohms meter check the wires. If you have one or more with excessive resistance that could be the problem. Or if they are five or more seasons old change them. I would check the timming too.
Back to basics..