Hey stripe listen. Redirecting to stripe.com is STRESS but its good for users because of security.
The overlay can (and would) easily be imitated by crooks who want to steal credit card details.
It would be much safer for users if you offer a paypal-like service where you store their credit details before hand. If you do this, then this is what should happen.
If the users has already logged in, then the overlay would simply be selecting the amount to pay (which coincidentally is shorter for users) and optionally, which source of fund to deduct from if user has multiple credit cards stored.
Security of funds is more important than ease of use.