I wouldn't say that you have no chance at a BT card at all. However, looking at your balances, I think it would be unlikely that you would get a CL that would cover all of the $38K that you currently carry across all three cards. The conventional wisdom is that when you apply for new cards lenders tend to give you CLs that match what you currently have. So if your cards are maxed, you are unlikely to get a card that's 3x your current limits. The best case scenario you can hope for is perhap a card that will match your existing limits if you are approved at all (that's a substantial if).
There are 2 strategies you can take right now assuming your tax refund and regular payments can cover it (I'm assuming a tax refund/regular payment of at least $12-15K):
1. Throw about 5-6K at each card, which would pay them each down to 50-60% level. That may be enough to get you a BT card that will cover the rest of the balances on your two highest interest cards (Chase and C1). Then I would snowball the remaining balances by focusing extra cash on the BoA and when that's gone, pay down the BTed balance before the 0% period is up.
2. Don't apply for a card, start snowballing right away. Concentrate extra cash on your balances starting with the highest interest one and move on down. When you are approximately 50% paid off, get a BT card and restart the snowball from there.
