We could have been at the summit around the same time - me for fifteen minutes around 2:00 pm, yellow KAS/Mavic jersey and then yellow hiz-viz Castelli jacket, dark blue Cannondale road bike.
I can't actually imagine riding the climb with a single speed. Are you geared at, what, 42 x 16 (70 GI)? Ouch.
On the descent, I saw another single speed rider, who might have been lhbernhardt.
My theory, entirely unscientific, is that gearing for climbs should be chosen such that one's legs give out at the same time as one's cardio (lungs and heart). If the legs go limp while the cardio still feels good, then you've left cardio "on the table" as it were, and should spin a lower gear. Conversely, if the heart hits redline while the legs still feel good, then you've left some legs still un-used, and should push a bigger gear.