If Glen was starting from LA, he would most likely go through Flagstaff. If he went through Phoenix, he would have to proceed east on Rte. 60, a narrow two-lane highway through the mountains and eventually pick up Rte. 66 somewhere west of Albuquerque.
Texola, just over the Oklahoma line, is about 1200 miles from LA. I drove about the same distance in a day, from LA to Boulder, Colo., but it was in a modern car and mostly over Interstate freeways going abut 80 mph most of the way. You couldn’t do that in 1967.
My longest day’s drive was 1000 miles, but it was all on interstates. I don’t remember how long it took me, but it was long enough that I couldn’t imagine adding another 200 miles.