Everytime I hear backfire at the exhaust and carb I think timing chain or rounded cam lobes. Your problem sounds like an ignition one though. Could be fouled plugs due to seals or fouled as they are not firing correctly. A cracked distributor cap could cause the problem but maybe it's just two bum plugs. Wouldn't be the first time. I chased a similar problem myself and traced it to plug wires, they looked good but were shorting through the insulation to the rocker covers.