You shouldn't try to block transactions when something you never did shows up, you should report it as fraud. If they got your number, somebody else probably has it too. Trying to "block" probably got you put in the wrong pipeline.

I had a similar experience with a (quite popular but not google) website provider that I had a relationship with and had given them my CC. At some point my account credentials went invalid - I could not do a password recovery no matter what I tried. Since I could not log in, I could not cancel the subscription. I emailed them and got no response. I could not contact "customer service" because I had to log into the site in order to do that.

After two years(!) of charges (charged once a year) and no responses, I got fed up and contested the most recent charge on my CC. I was contacted via email the next day by a customer service representative who was pretty unhappy with the chargeback and threatened me with cancelling my account. Exactly what I wanted - problem solved!