Matt Kirk ran & hiked the trail in 24d3h50m on July 1-24, 2011. Kirk's trip was basically thru-hiker style, which we consider to be in the "self-supported" category, but apparently he did have some help from family in the second half (see below). Links to Kirk's TR are now broken.
Kirk has these things to say:
I wish to inspire people of all ages to break free of the self-destructive habit of driving everywhere and get out and use their original God-given vessels, their bodies, for transportation. There are a million excuses, and some of them are fairly legitimate, for remaining encapsulated inside a car. But the benefits of walking, running and biking are undeniable.
I like to hike.