I think that there is no way that you will be able to remove the existing
3-piece surround and re-use it. It will crack no matter what you do, and
even if you were able to get it off in one piece (which ain't gonna happen),
it would have globs of glue on the back and won't go back in place
correctly.
With a tile tub surround, people sometimes remove the bottom layer of tiles,
remove the tub, then replace the tub, and put a new bottom row of tiles
back -- usually of a different but compatible color or pattern.
I doubt that you could do something similar by trying to cut the bottom inch
off of the plastic tub surround, leave it in place, remove and replace the
tub, and then put some kind of bottom border along the top of the tub. I
think that won't work, but if you feel like giving that a try, you could and
let us know what happens.
I say, good luck, and good bye existing 3-piece tub surround and hello new
tub surround.