"only" 4,000 ft elevation gain?? u kidding me? that's a load of climbing for a fixie.
I routinely do that much in my geared roadie, usually takes me about 2 hrs (pros' record is about 1.5 hrs) over 24 miles on a local mountain. Whats your gearing? on the flats, crit-style I'd say it's completely doable but not when road turns up.
I'm not saying it's impossible but I'd still do it for the experience.
It reminds me of my last clandestine alley cat race, there were a couple of sneaky state champions, it was supposed to go for a full hr, needles to say I got chewed and spitted out the back 3/4 of race