Been doing some tuning on the cold blooded , no starting, backfiring BF-750, here is what I have found to vastly improve them, the front carb comes from the factory with a 152 main jet, the rear carb has a 158 main jet, I have been putting a 158 in the front too, the other thing I have found is the air -fuel screws, under the silver plug on the bottom of carbs, drill the plug and thread a metal screw in it and pull the plugs out, set the screws at 2.25 turns out, the last one I did had one at 3/4 and the other was completely shut. While you have the front plastic off you can install the splash gaurds to keep the water out of airbox.

 

Above is a good info, especially on 05 model. However, if you are experiencing intake backfire, you may also want to install the richer needle jet (phycially narrower) in the front - use the same rear needle jet. In other words, you need two rear needle jets on the carbs. That will cure the intake popping & hesitation issue at low speeds.