This may be too late to be relevant, but my reply to a similar inquiry documents a straightforward shuttle option:
There is a cheap daily shuttle, which for reasons I've never understood, has not been well promoted in various GDMBR info sources. For about $50 you can get a ride in a van, with your bike in the attached enclosed trailer, directly from central Phoenix to the Antelope Wells border crossing in less than 6 hours.
I used this service to return from the border to Phoenix after completing the GDMBR north to south. You'll most likely be packed tight in a 12 or 15 seat van with no English speakers, so it might be a tad boring if you don't speak any Spanish. But the drivers are courteous and professional and the trip is very deterministic. Shuttles leave from Phoenix at about 6am daily. Contact Transportes Lozoya at 602-253-0843 or at 2208 N 16th St, Phoenix, AZ 85006. Try to have a Spanish speaker call them if you're calling . . . the person answering usually speaks very little English. Their shuttle business is largely based upon the many families that go back/forth between the Chihuahua region of Mexico and the Phoenix area. Its sort of a random convenience to bikepackers that the path of this trip is through the Antelope Wells border crossing.
With a noon to 1pm ish arrival at Antelope Wells, you'll have ample time that day to ride north 45 miles to Hachita.
