Different way to move Player-Entities

This is surprisingly difficult. I tried many different things, and everything seems to have a drawback. With this solution, the only drawback I could identify so far is that you will get problems if you stand in the "wrong" spot ("between" blocks on a multi block elevator). My workaround was to move the player to the center of one of the blocks that he hits.
Also note that more than 10 or maybe 16 speed-upgrades won't make a difference when going up, because I had to add a loop to move entities in smaller increments - otherwise they would be "overtaken" by the piston, hit the hitbox, and be unable to move upward.