Lady Scarlet gives some sound advice in what she said.

You might also consider the following where CARD1 = 2500, CARD2 = 2400, CARD3 = New Card with lower shiny interest.
CARD1 -> BT to CARD3
After CARD1 has a $0 balance call CARD1 company and ask for a lower APR.
If they give you a lower APR on CARD1 -> BT CARD2 to CARD1 and sock drawer CARD2
If they don't take CARD2 -> BT to CARD3 which is what you were going to do anyway.
After CARD2 has a $0 balance call CARD2 company and ask for a lower APR.
If they give it to you then BT back some balance from CARD3 and save your credit score.
If they don't sock drawer CARD1 and CARD2 and just know your credit score is going to suffer from the high balance to limit ratio on CARD3.
- AZQ