A VPN would be the only option to keeping them completely blind? I can set up a VPN on an Amazon micro instance for free. The amount of data used should be nothing or mere pennies per month to Amazon.
The only trouble is keeping a VPN up. I find on an iPhone at least that while once working, it works reliably, but keeping it working is unreliable. It seems when you transition from one network to another, one wifi to another, one cell tower to smother, or from wifi to cell and vice versa, the connection can often drop.
I wish there was a setting like "auto connect VPN when any data request is made".
I've tried VPN's from Amazon of my own creation as well as the VPN included with my GigaNews account.
I'm sure running the VPN on your mobile is great for battery life.