It would be possible, but difficult.
One correction: Your poor credit is not a result of the housing crash in south Florida. Your poor credit is likely the result of your not making payments that you had agreed to make. I'm not trying to be difficult or picky, but it's important to recognize what the real cause of an issue is. That's especially the case since you note that you and your wife have been working for the same employer for over 10 years, so the issue isn't one of job loss. People control their own destinies.
Your best bet is to find an individual who wants to rent a property (as opposed to an apartment complex). Recognize that your credit will still be an issue, and you'll have to demonstrate to the satisfaction of the landlord that you'll be able to make your monthly rental payments as agreed upon. You may also be asked for a larger-than-normal security deposit to help offset the risk.