There's actually a semi-optimal strategy that nearly guarantees winning if you're diligent about it. Just build a stairstep pattern with the highest numbers in the bottom corner of the stairs. Then basically combine sideways and downward and "always" resist the temptation to push up. Its kind of how some tri-diagonal matrix algorithms work. The only problem is you have to be fastidious about never using the one direction you've reserved as your excluded case (Up in my example) as that can screw your staircase by putting a [2] right underneath your wonderful [1024]. Just move blocks back and forth, waiting for the right blocks to create combo patterns, while generally storing lower cost blocks on the outside of the stairs, and then snake them through the stairs when you get a chain set up.

Ex:

x x x 2

x x 2 4

x 2 4 8

2 4 8 16