If I understand your plan correctly, you'll have a week to get to NM, a week to explore the state, and then another week to get home? That sounds like a fantastic trip to me.
The notion that it takes more than a week to see the state doesn't make sense to me. Yes, of course it takes a lifetime to really explore a place. But you can see and do so much there in the span of a week.
As for the 300/mile-per-day pace, I think that's a doable average depending on your own comfort level and your traveling companion(s). You could easily put in a 500-600 mile day to buy yourself some extra time on other days.
I live in the west and can't really speak to your route (which is what the OP's question was and what this specific forum is supposed to address), but I'm not totally unfamiliar with the area either.
This past fall we spent Labor Day Weekend up in Angel Fire (outside of Taos) and then drove our son up to Denver so he could fly back to school. From there we drove across Colorado, Kansas, Missouri, Illinois, Indiana, Kentucky, and Ohio. We absolutely loved that route and wished we had given ourselves more time. We had to get to Sandusky by the weekend because Cedar Point was only open on the weekends by then. After the weekend at Cedar Point, we looped back through Ohio to get to northern Indiana (Elkhart) for some badly needed repairs at the factory.
The drive through those states was pleasant and the roads were decent. I'd absolutely do it again.
Have fun with your plans and stay flexible. And as far as destinations in NM, start a post in Campgrounds and Attractions. You'll get plenty of great suggestions over there.