I think that someone who doesn't want to give their real email address to try out a service is even less likely to trust an unknown service with their credit card number. There are just too many "free trials" that promise to not charge your credit card and then make you jump all sorts of hurdles (e.g., having to call) to cancel the free trial.
I think you'd be surprised. Credit cards are easier to dispose of then email addresses, and they offer greater protection with fraud and billing dispute processes. Some banks even offer virtual cards that let you set limits on duration or amount.
And that's OK. The problem as I understand it is that people are signing up with disposable email addresses, using the API key they receive for 7 days, and then signing up again. They are leeches, exploiting the generous free trial.
If they stop signing up, no problem. Other people who sign up with a disposable email address can test within the restrictions, and once they trust the service have a choice to enter card details or not. If they are planning to do business with the service, they're going to have to trust it with card details.
Suggest using the Standard plan but with significant rate limiting. Like 5/day.
If they want to remove that, enter credit card details which you verify.
You can still have the trial expire and the credit card isn't ever charged; but you can track people on trials more easily.