Disputing the credit card transaction for the original purchase is worth a shot.
As a general rule, do not try to initiate a credit card dispute or chargeback with any company you ever intend to do business with ever again.
This is not a bad idea. This is the only idea that actually hits the company where it hurts and puts pressure on them to not do the same mistake in the future.
Furthermore, suggesting this to someone without preparing them for this outcome is an aggressively bad idea. If someone is cool with cutting themselves off from Google, great, but they probably should be preparing for that long before they issue a chargeback and discover their email account gone.