All sorted. Yup, it was that "oh, that's your billing name? lemme change your name 'cause I'm iTunes!" thing. Rang straight through when I called, they poked around a bit, then they were able to sort it out and attach my payment to that enrollment.
Already, I can check it out in the Dev Center - no longer shows "Pending…", but my actual name. Yay! Now I think I need an icon and some Web stuff before I can push stuff up to TestFlight…