First step: Remove its status as the Icon. Redo the Chinese Theater as I've mentioned before to make it an opulent, "generic" 20s/30s Hollywood style theater, and make THAT the Icon.
Second step: Move the Hat to the front of the entrance to the Animation Courtyard. Right now the Disney-MGM sign is there. Since that name is going the way of the dodo, take the whole thing out, eliminate the Mickey hand tipping the Hat, set the Hat down on the ground, carve out a walkway through it (they might even be able to still have a dippy pin store in it), and the Hat can survive. Heck, they could even leave the hand in it still tipping the Hat. It just won't look quite as balanced...like now. With the Hat over there it will not so easily mess with the 20s/30s Hollywood look the "main street" was originally supposed to have.
Third step: Enjoy.