Stay FAR, FAR AWAY from ANY exit company. What they do is charge you, then put an ad for an exorbitant price on some obscure website, then when it doesn't sell, they charge you again to re-up saying that they did their part.
Better to let it go to default and take the credit score hit. When you recover, you can rebuild your credit and move on with your life. If (when) you get an unfavorable on your credit report, you can write a mitigating letter that HAS to accompany any credit inquiry. These days, creditors don't really look too poorly on timeshare defaults.
First things first. Get well, get employed. move on.
All the best!
Jim