[chandler48]

It sounds drastic, but your door needs to be raised, frame and all to bring it all above the tile. Measure the height you need and make a "shim" for lack of a better word, to go under the threshold and apply a door pan over it, then set the door back in. You "should" have room at the top, but the age of the door tells me you may not. Often door framing pretty well matched the door jamb size.