Buy a $20 used phone and get the cheapest pay-as-you-go plan you can find (you'll only be using the phone to receive text messages, so it should be really cheap) and consider it a somewhat impractical Google Authenticator hardware dongle.
Note that even a cheap, pay-as-you-go phone emits a breadcrumb trail of mobile network (and possibly GPS) location information. Unless you power it down between connection attempts. In which case it still emits breadcrumbs, though fewer.
