Is exhaust back pressure the culprit here?

You will be at this for a while if you don't get a plan. There are many easy checks you should start with. Fuel filter, fuel pump, maybe a wire going to ground intermitently, damaged plug wire, maybe while the anti sway bar and pipes were being banged around back there the fuel line got damaged. Look down the carb with a strong light and see what it is doing. Distributor tight? Poor fuel milage? Just some thoughts. You get the idea.