If it was via a credit card, consider doing a charge back. Sounds like you have plenty of evidence that they didn't provide the service they claimed they should have. Even for a small amount it hurts them much more with the CC processor.
It is a pain to install apps and use an Android phone with play services installed but not logged in.
...or just create another Google account in a fake name.
You seriously think that the company that knows more about you than most intelligence agencies can't tell if you're hoodwinking them?