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Couple things about your $2k and paying off the 3 promo's:
1. It should apply in order they are going to expire.
2. You need to pay OFF each one in full... it doesn't matter if you pay half or 90%, if it's not 100% paid off on exp. of that promo you will be charged ALL the accrued interest, so I would go in order that they currently have them and try to get A and B gone or at least A and half of B and cross those fingers you can balance transfer, cash advance, temporarily overdraft your checking account to cover at least the rest of B before that exp. of the promo.
I am very, very, very, very sure that I can have either A & B or C paid off by their respective expirations. And I think my odds are good that I can BT the balance of whatever's left, even if I end up having it spread out over 2 or more cards. Last card I applied for was the USAA Amex, I got $4000 and my score's gone up since then.