I would start with 135 main jets, 42 pilots and throw a couple of shims under the needles if they are stock. Better yet, get a couple of needles out of the older Triumph Thunderbire (TBS needles) and use those or the needles out of a Thruxton.
Pull the float bowls off and see if you can tell what jets you have in place. Since it's always run funny, I bet the bike was never jetted properly.
One way to see if the bike is lean, throw the main snorkel back into the airbox and see if the problem goes away.
