Submitted by Danny Naylor:
Among runs available and searchable on Strava, this run by Shelley Chestler appears to be the fastest time for the complete* loop in the counterclockwise direction, and the fastest time overall in either direction. The time submitted is the total elapsed time for the run and is not based on any Strava segments, although I used existing segments and one of my own making to better confirm this as the fastest time on Strava.
*Asterisk* This looks to be about 2-3 minutes shy of the complete loop, presumably starting at her car away from the trailhead, then finishing at the trailhead proper. I'm still submitting this as the FKT for now as it is still considerably faster than any other woman's time on Strava. I would say that anyone completing the loop in under 3:35 has a strong claim to the FKT over this time.
I'm submitting this as "unknown" style. The run was completed with a partner, Martin Masonpierre. Based on the standard rules, this could be considered "unsupported, accompanied" if no muling took place, or either "supported" or "unsupported, mixed gender team" if anything were shared between the two.