Wasn't something I mentioned earlier but using the reCAPTCHA audio is also another solution for gcap. I haven't ever used it personally but always seemed like a cool idea.
It’s also very satisfying to know I’m not an unpaid mechanical Turk for google anymore and that it’s a machine solving another machine’s challenge.
Still pretty expensive if you wanted to do every single Valid CC #, though.
This one in particular is simple enough that nearly any technique you wanted to throw at it would succeed with minimal fine tuning. I'd be shocked if it took an afternoon even if you'd never broken a captcha or done any image processing before, and that's without borrowing an off-the-shelf ML solution.
Plus, even if you had a 50% failure rate you'd just need twice as many calls. That's not trivial, but it doesn't really affect the viability of the idea.