I know you didn't put this in your list of options but would you consider taking the 405 from LA south to San Diego then I 8 east to I 10 then onward to Texas? The traffic through LA on I 10 can be/is horrendous until you get out of the metro area. (Riverside) In March as previously mentioned portions of I 40 can be closed for days in severe weather. (expect it because its the right season and this is an El Nino year) Taking I 8 keeps you well south of the higher altitude cold weather plus you get to see the coastline to San Diego before heading east. The only hilly section +-4200' MSL) is just east of San Diego for about 75 miles until you hit Imperial County. (very doable) I've done it many times in my 30' class a gasser. Then the route is fairly flat the rest of the way. Your choice. Enjoy.
P.S.: I agree with barmcd. I 40 is horrible around the Flagstaff area. I was just there two months ago. Very rough!
Chum lee