Thanks so much for all the tips! I really appreciate the voice of experience.
My plan is to do the Great Divide offroad route, so I want to take my Surly Ogre, no folding bike on this trip. Since none of the NM stops are baggage stops, it looks like my only option is to get off at El Paso and bike to the route. It's about 150 miles on pavement, hopefully there's a route that's not too bike-unfriendly.