Continuously build up a specific square^, so this one I just kept moving things from the bottom right 2x2 up-and-left into the top-left 2x2. I avoided pressing S or D as much as possible (i.e. only when it was literally the only move I had, and then I'd press D (or S) once and continue as before).

This means that the sum of the top-left square is strictly increasing, and so "eventually" you'll win (assuming you don't fill up the rest of the board before that).

^In this case a "square" seems like it can just be one of the 2x2 ones, but in the original 2D case, this strategy has focus on building up just a single tile (one of the corners), or it doesn't work.