The thing is I always pass the enrollment step, it's paying for the membership that blocks for some reason. I think it might be the Apple Store's fraud system that flags me for some reason, rather than an issue with Apple Developer itself. Regardless, thanks for the advice.

Maybe try enrolling on your phone instead of your desktop. I had a mighty battle with AppleTV recently trying to sign up for Apple TV (which I would guess uses the same payment system). I suspect the root issue for me was that my copy of Windows boots off a non-encrypted drive, and was being considered as a non-secure connection. (I'm dual-booting with an older version of Ubuntu).

Anyway. Paying on my phone worked the first time.

Create an Apple Pay account with your cards or maybe you can pay with PayPal?