Update
I called B6 back, and the agent told me there is a fee. She was very nice, but adamant. I explained that on her end, she is doing everything right. But that on the customer's end, there is a glitch.
I asked her to leave things alone, as I wanted to write JetBlue and explain the problem.
She then did some typing, told me she would waive the change fee, and re-issued my ticket.