Hi,
I can only add a couple of pieces to the puzzle.
First of all, unless you REALLY hoof it, you'll need a couple of stops between ABQ and NO, no matter which way you go.
If you head south on I-25 at ABQ to I-10 near Las Cruces, NM, you can basically stay I-10 all the way...but, there is nothing (and I mean nothing) between El Paso and Kerrville except Fort Stockton, TX. There's got to be RV parks there in Ft. Stockton, but we've always motel'd it. Generally, Fort Stockton is 8 hours out of Albuquerque. Kerrville is another 3 & 1/2 hours past that.
From Kerrville on (still another 600+ miles to NO), you are more or less in civilization (except it's TX and LA, of course) from there to New Orleans.
If you have anytime to stop and smell the roses along this route, I recommend the Texas hill country in the area roughly formed by I-10, I-35 and Hwy 290. Lots of unique places, but being in a hurry isn't allowed in that part of the world.
Have fun,
Other Ron in Albuquerque
Listening to:
the almost full moon