Comment by chidevguy

I was able to get 2048 building off of your solution. As you said, always keep your highest number in the top right corner. Try to build the next highest numbers up along the right edge, so that you have say, 256, 128, 64, 32 along the right edge. Always keep 4 numbers there, and only use up/down/right. Then just focus on building whatever number you need next to double the bottom right number, so that you can "chain up" numbers along the right edge and double your highest number in the top right.

Kind of hard to explain in words, but hopefully that helps!