Considering your situation i would probably app for an AmEx card, as it's possible to get 3X CLI after 61 days. YMMV
Then you'll be able to split the amount between two card if Discover is eligible for 0% offers. If you BT only to Discover it would put you at almost being maxed out, which will lower your score. And would also require sizeable payments so as to not worry them too much.
I would ceck with Discover to see if you have BT offers, then move $2,200 over from BoA Alaska. Then app after the new balance reports.
Also might check into a CLI for the Alaska card, I heard they were SP's now.
All other card generally cannot get a CLI until 6 months after opening, so if you get a small CL, you'll be in a spot if it's not large enough to absorb said BT amount.
I'm not sure how much of a role that existing dept consolidationloan will play, not to mention BoA Alaska being at 70% utilization. It could lead to getting a lower SL than needed.
