Good question about the 22 ns. Unlike the airplane experiments, because the van traveled slowly (60 mph max) and only for a few hours getting to and from the mountain, the relativistic effect due to velocity alone would be about 0.05 ns, or 50 picoseconds. Too small to worry about.
The dominate effect for this experiment, since the van and clocks just sat still a mile-high for the weekend, is the gravitational relativistic effect. The GR time dilation rate is approximately gh/cc, which for an elevation gain of 1340 meters and a stay of 42 hours, comes to about 22 nanoseconds.
More info on the trip is at http://www.leapsecond.com/great2005/