Sorry for the delay in commenting. I have been away for a couple of weeks.
There is one other possibility.
Have a look at this post on my blog:
http://barlaventostravelblog.blogspot.com/search?q=auriga
You could make your way down to Faro Airport by bus/train from or hire a car at Lisbon Airport from some one like Auto Jardim, drive down to Faro Airport, drop it off and then pick up a Auriga car.
Web site here:
http://www.aurigacrown.com/
