Instead of webpayments.io (is a nice solution, but...) it would be better to have the possibility like the custom domain for customer but here for us. Setting up a CNAME record pointing webpayments.io and charge our customers within our own full domain name, that gives more trust to our customers and is more elegant and nice for us. For example "secure.example.com" when the customer receive the payment link
Here is an example --> http://d.pr/i/artd
Have you tried site masking or an iframe?