The Leidenfrost effect has been observed for liquid droplets, which take longer to evaporate because of the vapor layer formed below it. Has it been observed for other phase transition? (ice to water where the ice is separated by a layer of water.) Can someone theoretically prove or disprove the existence of Leidenfrost effect for other phase transitions?
Alright, I did a little bit of googling, and found two quite interesting articles on the subject. Since you originally asked for a Leidenfrost effect in "...other phase transitions.", I think these examples will be sufficient.
Phys. Rev. Letters has a paper on modeling the Leidenfrost effet for granular materials, glass beads in this case (accessing this from my University network, not sure if it is behind a paywall). The gist is that you can model a Leidenfrost effect by vibrating a shaker fast enough to achieve a supporting layer of very fast, diluted ("gas-like") beads that support a layer of beads that are densely hexagonally packed (like a crystal).
However, I find this review here much more interesting. Figure 1c in particular shows a piece of dry ice (i.e., solid CO$_2$) hovering on a thin sheet of sublimated CO$_2$ gas. (Hope it's ok to use this image here.)
So, the answer to your question is yes, there is a Leidenfrost effect for other phase transitions than liquid-gas, and also for other materials than water. The follow-up question of whether this can happen to ordinary water ice is then, I think, answered by the phase transition diagram (from Wikipedia)
So we just need to cross directly from the ice regime to the gas regime, which can happen below the triple point of water ($0.01^°$ C, $611.657$ Pa $\approx$ 0.6 percent of atmospheric pressure), so you'd need a pretty good vacuum to achieve that (so long, dreams of just firing up a pan outside on a Bunsen burner to test it out).
Hopefully this is sufficient enough for an answer :) cheers!