This is what's left, and I've been paying the cards Dave Ramsey style

I assume this means, the lowest balances first?

Unless you have cashflow problems (and if you have a spare $1000/month, it doesn't sound like it), you should pay off the highest interest cards first. Here's the mathematically optimal way:

July: Pay the usual $1000, plus the $4700 bonus, towards the 14.99% loans. (This will kill the smaller one off and make a dent in the bigger one).

August: Pay the usual $1000, plus the $1500 bonus, towards that 14.99% loan.

September: You just have $1000. Pay $500 towards the 0%/21.99% loan, and $500 towards the 14.99% loan.

October: Pay off the remaining $1000 on the 0%/21.99% loan, this will be just before it starts collecting interest.

If the dates don't line up, move the $500 and $1000 payments on the 0%/21.99% loan back by a month.

From there on, put all money towards whatever loan has the highest interest rate, where the remaining 0% periods

*do not count*. That 14.9% loan is still 14.9%, even if it's not collecting interest yet; you want to minimise the time during which you'll have to pay 14.9% on it, so start paying it as soon as the 14.99% loans are paid.