Securing the payment page

Using hooks, there’s a way to add a honeypot field to the checkout form and a function to its validation, but on the payment page, none of these apply, and I see no relevant filter or action hooks.

Is there a way to add a honeypot field + validation to the payment form to secure the payment page? Ideally, there should be a way to add this only on the payment page, because the checkout page is already covered.

Similarly, how can I secure the payment form with a captcha?

The page I need help with: [log in to see the link]