Found this out when I took Luigi through Bowser's castle... not going to tell you how, you'll have to figure it out. Anyway, I was Luigi through the climb, Mario through the cutscenes, and during the fight, I was Luigi till I grabbed bowser, then I became Mario for the throwing . Weird, huh?
This is because Luigi did not have any throwing sprites programmed into the game, as it probably was not intended that you be able to play the final level as Luigi. But it's better than having the game freeze, huh?