I (Jessica Kelley) completed this route on Oct 26, 2015. Like Christof, I did it unsupported, which included carrying all the water I needed for the traverse. It took me 10:02.
As far as I know, I'm the first woman to do this route unsupported. I’m hoping another woman will come along and put in a real effort at an unsupported FKT. If she does, she will almost certainly beat my time by a couple hours.
Running alone through the desert at night is a cool experience! Give it a go!
Blog post and Strava link here: evergreenendurance.com/2015/10/27/trip-report-joshua-tree-traverse-aka-37-miles-for-my-37th-birthday/
Jessica Kelley at the start of her JT Traverse