Payment form submission is returning a curl error! ([curl] 3:  malformed [url])
For those interested, here was the solution: The payment method for Authorize.net wasn't completely filled in; there was no endpoint set. Thus, it was of course failing when it sent the curl request, because there was no protocol, domain, or anything else other than the query string for the payment form.

Providing the payment method with an endpoint in the CP resolved this issue.