Debt and Savings

First off, transferring isn't going to save you. You're not able to get a high enough balance because you're already at risk in the creditor's eyes. They can see that you're not "caught up" or aren't able to pay your current debts. 

HOWEVER, that isn't the problem. The problem is that you're running from your debts and financial obligations.

I understand how you must feel that you're in deep water and are sinking. From your message, it seems you think that credit cards equal money and the more "random" cards you can access, the more money you have at your disposal. But this is far from the truth and is just what your creditors want you to think! Credit cards do not equal money—they're the opposite of money. They're the loss of money at some future date.

First things first--stop using your cards altogether. Then choose one. I like to choose the one with the largest balance. However, if you have others that you know you can pay off in a few months, then pay them off first and concentrate on the other debts later. You might even be able to renegotiate your terms with your creditors.