Could you wear a camera vest with lenses, filters, flash and small reflectors in the vest's pockets?
Some travelers wear a vest with their sport coat or winter coat. Why not a camera vest?
Your tripod could be inside your checked luggage.
If the camera vest is not feasible then I'd look into shipping the camera equipment you plan to use to the address you'll be using in New Mexico.
If you decide to check your camera equipment, a hard-shell, waterproof case will probably provide more protection from rough baggage-handler and conveyer-belt handling than a soft-sided case/backpack.
Hope this helps.