Leafing through Herbert Ungnade's classic Guide to the New Mexico Mountains (1965), I happened to find a short section on "Climbing Records":
The speed record on the La Luz trail to Sandia Crest was broken in July, 1964, when Charles Floading from Sandia Base climbed to teh top in 1 hr., 25 min., 20 sec. Only a month later Dean Rickerson from Los Alamos made the same climb in 1 hr., 8 min. Floading made the Wheeler Peak climb by way of Bull of the Woods Mountain in 2 hrs., 11 min., 20 sec., while Rickerson climbed by way of Williams Lake in 1 hr., 8 min. Dean Rickerson also holds the speed record for the climb of West Truchas from the boundary fence at the irrigation canal. His time in August, 1964, was 1 hr.
1:08 on La Luz is solid -- the winner in 1965, the only year before the course was changed, was 1:20:44. 1:08 for Wheeler is also pretty solid, though it's unclear where Rickerson started. Ungnade states that "it is possible to jeep the first 2.5 miles" of the 4 miles to Williams Lake. I don't know where the boundary fence was along Rio Quemado on the way to West Truchas.