When you said "40 Mile Desert," I thought you might be referring to the Black Rock Desert (where the Burning Man get togethers occur), but I see it is not the same place.
Regarding your chronograph, I would make a couple of wood shields three or four feet square, with holes maybe twice shot diameter (maybe bigger depending on group quality) and place them in front of the barrel. First one maybe 5 feet in front and second 5 feet farther, with the Chrony just downrange from the second shield. Use sturdy supports for all as the muzzle blast will try to knock the shields over, especially the first one. You may also need a V-shaped deflector over the Chrony (point toward muzzle, space between the legs over the chronograph screens) to split the smoke at the chronograph.
I know, just what you needed, more junk to take with you. (-: