A problem with theory that God reversed time for Hezekiah's miracle is that Hezekiah and everyone else, including the Babylonians, are caught in the same space-time as the Earth. So if God rolled time back, Hezekiah and the Babylonians wouldn't notice it because they would be rolled back with it, else they would suddenly find themselves hundreds of miles from where they were a minute ago. (If the earth went backwards and they stayed in the same place.)
If God increased the Earth's inclination by a few degrees, it would move the shadow back. It would also change the climate. Velikovsky cited some evidence from Egypt that the length of the day on the solstices in Egypt was much shorter than would be expected prior to 700 B.C. The climate of Palestine and much of the world at that latitude started drying out and becoming desert around that same time period in history.