One explanation is that ol’ Palps levitated himself onto a walkway down the elevator shaft after shooting blue ribbons out of his hands and then hopped onto a shuttle.

Another possibility is that his body landed on a catwalk and a Praetorian guard found it and got it out on a shuttle for future reanimation.

Or if you wanted to get really crazy and use clones, the Palpatine on DS2 could have been the clone, explaining his clear insanity.

The absolute worst way to go would have the original body die and bring him back as a clone.