I've checked out the capabilities of the Google Drive in terms of programmatic access. Here is an example for the main game file:
Luckily GD has this host feature for a public directory where each file and subdirectory can be accessed by its proper file name instead of the cryptic File ID (this allows even hosting web pages).
So, the procedure will be as follows: game files will be kept on Google Code site, but changing bits will be now served from my GD account. One drawback is that there is no download counting on GD yet.