I don't think it is impossible, since you control Kafei one time on his side quest (Sun Mask huh? How I love Zelda...) and the game has funny glitches, as I heard (I can't comprove by myself, I still did not try them), like to control the Fierce Deity not only in boss rooms, but in Termina Field and use the Giant Mask in the Sakon's Hideout (what may cause crashing). So, I think there's still some hope.
PS: [offtopic] I finished MM one time not using the FD mask. Ok. Then I went to moon again to battle Majora (using the same save state), and this time I used the mask. But hey, that mask makes Link act berserk it isn't? But why can I control the FD Link normally, like controlling the kid Link? [/offtopic]
Ah, I have this state. If you guys want it, just tell.