Check the air cutoff valves on the carbs. Those valves could be checked without taking out the carbs. Mine never stopped backfiring and I know these are the culprits, I just haven't replaced them. You can find them for about $35 each set on eBay, including the spring and the tiny o-ring. You could also find them on other motorcycle parts sites, but if you're only buying one or two parts, it might be cheaper on eBay.
1985 VN700 unknown mileage (over 33K)
Iridium spark plugs
NGK wires and caps