American General, CitiFinancial, Wells FargoFinancial (not Wells Fargo Bank)- they do these kinds of loans. Sounds like you have good credit.
I got a 5300 American General loan a couple years back. It's not "unsecured"- it's "secured by household goods"- same damned thing! They write down the value of everything you own- TV, computer, DVD, Nintendo, Playstation, sofa, etc. If you pay all the payments on time, great. Even if you don't, I don't think they will come and clean out your home. They don't want our used junk. I think it works similar to a secured loan.
Sounds like you have good credit, but a bank will not help you. You need a place like these. You are on the right track with the suggestions you made yourself.
And of course, I'm sure you know the interest rate will not be low. Everyone here will chastise you, but if you need the money, you need the money!!!