Thanks to everyone for the advice on both sides of the aisle. I really appreciate the time you've all taken to help me.
I have not made a decision yet, but I'm leaning towards accepting the offer, as I believe I can pay down the Wells Fargo loan very aggressively ($600 per month at the very least, as that's what I currently pay between the auto loan and payments on the three cards I'd be paying off). WF online banking also allows you to specify that a payment be applied to principal only. I do understand the risk I'm taking with regard to being very upside-down on a very old car, but it has been extremely reliable. I'm not too worried about losing my job or a repo, as I think that risk is much lower than the reward of paying off the cards and lowering my revolving debt. I'm healthy and have never been fired or laid off from a job in my nine years in the workforce.
Would anyone be able to assist me with the best payoff strategy/timetable for the balances if I do not end up going with the refi?
As far as how I got into this situation and controlling spending, I did have a couple of short periods years ago where I had to "live off of" cards due to unplanned expenses and no savings, as well as some significant cash advances to assist immediate family in emergency situations (I know that's a bad idea, but I couldn't refuse to help family). I haven't made any purchases on any card in the last six months, and very few in about a year. I am serious about getting the debt paid off and do not plan to charge them back up again once I pay them down. My only major weakness is eating out a lot, and I've already begun to curtail that. I haven't even bought new clothes, shoes, or any electronics/luxury purchases in as long as I can remember. My question about CLDs was strictly from a credit score perspective - I'm not interested in having the credit available so I can use it, just so I can lower my utilization.
I hope this information gives you more insight into my situation, and I'd appreciate hearing if it changes any of your opinions and advice 
shadow2k: I am definitely not carrying the balances just so I don't get CLD'd. I understand that would be a ridiculous strategy. It's simply a matter of not being able to pay much more than the minimums with my current income and interest rates.
Thanks!
Thank you, Andre. BTW, I did not take offense at your previous message I understand I'm in a pretty horrible situation and I'm not looking for anyone to sugarcoat it for me; just trying to understand my options on how to get out of it.
I was under the impression that gap insurance was only available at the time of purchase - it's something that can be added to a policy for a vehicle I've had since 2003? I'm with State Farm.
Here is another option... Call up each of the credit card companies, and ask them if they can lower your interest rate, even a temporary decrease for 6 months. This way you don't have to take the refi option from wells fargo and could potentially get a rate lower than the 18% on your credit cards that are higher than that. Then like the others said, just apply larger payments (from the money you were spending on your car note) to the credit cards with the higher interest rates and you will be out of debt in no time.
Current Score: Eq: 823 Tu: 830finally talked to the Wells Fargo guy again.. after he took my documentation to the underwriters, they refused to do any refi based on the age of the vehicle and mileage (he claimed that my credit was fine; it was just those factors).
I guess it's the traditional payoff route for me 
@Anonymous wrote:finally talked to the Wells Fargo guy again.. after he took my documentation to the underwriters, they refused to do any refi based on the age of the vehicle and mileage (he claimed that my credit was fine; it was just those factors).
I guess it's the traditional payoff route for me
They saved you from committing financial suicide. Stick with a budget and overtime everything should work out. Maybe take a part-time gig to help pay things off faster.