Okay, I can't say that I understand quite how I got it working. But I did.
I was able to one-button deploy it to Heroku, and using that server to process the payments, the test payment went through as a success. I'm not done - not by a long shot - but that's the really hard part. And it's done.
Right now, it's only set up to accept test payments. And it doesn't have auto-email confirmation. And it only works with $20. This is all something I can fix soon enough.
Most importantly, I registered the domain for this site. "SendThisGuyToCodeCamp.com"
"Hey, Carl, what's the address for that site about sending that guy to code camp?
"Send this guy to code camp?"
"Yeah, thanks Carl!"