You can certainly try, but besides the fact that you would need command support (which is not easy) I would love to be in the office, when you voluntarily ask to go from fighters to heavies... I can tell you that when Bullet volunteered to jump out of perfectly good airplanes with the 82nd, jaws were dropping all over the base.
Second, depending on where you are in your career it would kill you, because you will go right back to where the FNGs from UPT are, you lose your IP status, since you are not qual'd in that plane. You would be the same as a 1st lt entering, you will move faster, from actual flight experience, but you still have to climb up the ladder.
I do know of one other beside Flieger who had the ability to cross over from fighter to heavy, but it was a guy who injured his back in the 111, he was med dq from ejection seats, so they offered him to go to heavies. He was a major, and decided to not take them up on it, instead he went to the AFA and became an instructor, from there he was by name requested to become the OSS commander at Mt Home, where he pinned on 0-6 and retired. He never flew a heavy because it was more important to get the right job for promotions then flying any ac.