Wow, yeah, 19 hours is a really long drive with two babies, even if they do sleep a lot as newborns. That's a great thought about New Mexico. Yes, there is a birth center there that I've heard good things about.
Another option is Texas or Utah. I know midwives in El Paso who I could refer you to if you like and there are birth centers in Austin, though neither of those are very close to you either!
If you have already had a homebirth with a midwife I wonder about contacting your former midwife (if you had a good experience with her). Since you already have that foundation of trust and connection, she might really go the extra mile for you and perhaps she'd be willing to travel to a nearby state to attend you at a friend or relative's house or a hotel.
Midwives Alliance of North America's website has a list of CPM's all over the U.S. that you could check out. And you could also post a query for a travelling midwife (or one in your state of choice who is willing to attend twin homebirths) on the Midwifery Today forum online (just google either of those).
Best of luck and let me know if I can help you contact anyone...I'm a midwife in CA and also a mom of twins myself so I really feel for you!