If you compress the json first, it isn't quite so bad.

Example #1 (short string):

  input: 103 bytes
  gzip(input): 87 bytes
  base64(gzip(input)): 117 bytes

Example #2 (long string):

  input: 3122 bytes
  gzip(input): 840 bytes
  base64(gzip(input)): 1121 bytes