You are good to go in both NM and AZ afa riding with it concealed. Your license is good here in NM and in AZ you don't need one to carry concealed.
Read up on the applicable sections at handgunlaw.us regarding NV. They say: "Nevada law is silent on carrying unconcealed firearms in vehicles. They do have a law against carrying loaded long guns in vehicles. But no law against handguns."
That being said, regarding your question about lack of saddlebags- do you have some form of luggage, like a bag or duffel that you will have with you? If you have a locked container in a bag, that will serve the same purpose- as long as it's inaccessible to you and secured.
I would not open carry in LV. Just keep up your situational awareness and be careful.