There were two fixes. First, with the help of Daniel (tri4sale), I fixed an issue where the CVV2 begins with a leading zero. We were dropping those. He was able to get the affected card to work.
The other was that our payment form had one field for first and last name and I was crudely separating that. I noted the old site just asked for them individually, so I changed that as well.
Now if I could just get by BBT card to work on the other sites.