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I haven't done LA to Houston, but I did Indian Wells, CA to Houston in September 2016.
I went the straight supercharger route:
Indio, CA
Quartzsite, AZ
Buckeye, AZ
Holbrook, AZ
Gallup, NM
Albuquerque, NM (stayed overnight here)
Santa Rosa, NM
Tucumcari, NM
Amarillo, TX
Shamrock, TX
Weatherford, OK
Oklahoma City, OK (stayed overnight here)
Ardmore, OK
Denton, TX
Corsicana, TX
Huntsville, TX
Houston, TX
However, this was before the Childress, TX supercharger was active, so the route can be done this way now in a 90D:
Quartzsite, AZ
Buckeye, AZ
Holbrook, AZ
Gallup, NM
Albuquerque, NM
Santa Rosa, NM
Tucumcari, NM
Amarillo, TX
Childress, TX
Denton, TX
Corsicana, TX