Wow, sorry to hear this was your experience, original poster. But I gotta say: who judges a state's bicycling friendliness by riding the interstate shoulder from one side to the other? That's plumb insane, as my Pappy would say.
I just spent 5 days covering over 300 miles in southwestern NM and a tiny bit of southeastern AZ. Silver City, Hatch, Gila, Three Way, etc. and I can't tell you what a wonderful place it was. Perfectly maintained wide roads, almost all of which had wide well-maintained bike/emergency lanes, which we didn't even use because the regular car lanes were so deserted. Perfect November weather in the low-seventies, endless blue skies, friendly drivers and friendly restauranteurs, abundant and easily located stealth camping sites. What's not to love.
Not trying to argue, but I hope nobody reads this thread and crosses NM off their list because the interstates aren't particularly fun to ride.
I was a little surprised to hear negative comments about NM wrt to bicycle touring when my experience there was overwhelmingly positive.. It is good to hear that your experience in the south east part of the state was similar to mine in the north east part. Based on my limited experience there (maybe only 250 miles) I'd rate NM right up there among my favorite states. It was especially nice since it immediately followed some really lousy road in Oklahoma.