Changing your data structure for the sake of compression harms the main advantage of JSON: convenience.
Sample JSON Object, using this technique:
>>> Length (Original): 25565
>>> Length (Original, gzip): 3966
>>> Length (Using 90deg): 15626
>>> Length (using 90deg, gzip): 3633
So while the optimization gives you almost 10k bytes in size reduction, the gzipped result is only a 300 byte reduction in this example.
When you want speed - every byte counts right?