I managed to beat it following a basic pattern similar to yours:
1) Mash up-left (or towards any corner) until blocks stop moving
2) Press right
3) Start over
The trick is to keep the high numbers in the top corner so the new numbers don't spawn behind it, you basically start building towards that corner and things start to work themselves out.
Like you, I had to do a bit of actual logic near the end, you can see that I overshot by a small margin and ended up with a 128 block too....
This works remarkably well. There are some spots where you have to apply logic -- in particular, I found that I progressed best when I built out the top row with my highest blocks (and then push/cascade my next highest block into the top when it got to be high enough) and I occasionally had to mash up-right rather than up-left to make that happen.
1) Mash up-left (or towards any corner) until blocks stop moving
2) Press right
3) Start over
The trick is to keep the high numbers in the top corner so the new numbers don't spawn behind it, you basically start building towards that corner and things start to work themselves out.
Like you, I had to do a bit of actual logic near the end, you can see that I overshot by a small margin and ended up with a 128 block too....
http://i.imgur.com/NA92d3G.png