Air in the filter is not necessary bad. I've had bikes with filters that run with a "pocket" of air all the time - because a portion of the filter is higher than the adjacent line (air had no where to go).
If you open one of the carb drain screws, does the fuel still flow?
If you dropped two cylinders - I'd first suspect points/ignition. Were the two cylinders 1-4, or 2-3? If so, look into your ignition.