Sorry for the multiple replies --
So, a chunk of my debt IS on my NFCU; and while I'd love to get another card, I just asked for a CLI and they had to decline because of my overall debt amounts (which is why I'm trying to restructure a bit).
I did wonder about chunking off some of my present CLI on my card to another card, but I thought that wasn't possible? If it is, I wouldn't mind doing another card for a balance transfer, paying down a chunk of it and then transfering CLI from my big NFCU card first.