I recommend you recheck the valve clearance before going in another direction. It shouldn't be that difficult to find TDC and the mark on the flywheel. With the sparkplug removed, turn the engine over with the pull start while watching the valves. After the intake valve closes, the next time the piston comes to the top is when you set the valves - both intake and exhaust. You can verify TDC with a small screwdriver inserted into the plug hole but be very careful if doing this - you don't want to get it stuck/bent in there! Once the valves are set properly, if the backfiring still occurs, then look into a possible carb issue.