Player movement restrictions

Hi Everyone,

I am attempting to create a small prototype of the game Catherine. In this prototype the player stands on top of boxes and has to climb up them to the top to win the level. Whilst climbing the player has to move the boxes into different positions as they can only climb up one box at a time.

So far in unity I have set up my boxes and can set up a character place holder in third person. I would like the player to only move one box at a time and only in the front, back, left and right directions (no diagonal movement).

Should I move the character using transforms or via character control. If anyone could share some script examples, that would be much appreciated.

Here's a clip on Youtube, if you skip to around 5:00 You'll see the movement I am referring to

Here's a screen shot of my current set up: