I say do it as soon as possible!!, I mean even if you get pulled over in NM just tell them you're visiting having the peace of mind that your license still hasn't expired. Just make sure know the all requirements and that you have all your necessary paperwork with you (matricula, birth certificate) w/e they ask.
I encourage you go to visit their website and get informed before going.

I was in the same boat as you, I got informed, looked through the requirements and I was lucky enough to find someone to take me, (though I had to pay a hefty fee lol).
Just remember though, "Life without risks is no life at all"