When the Northwest Territory was carved up into states the federal government continued to own the land and they sold it off to settlers, miners and others over a period of time. The last open public land sold by the federales in Indiana changed hands in the early 1900s! (a good example).
If New Mexico wants to purchase the federal lands go to it. Do it the same way things were done in the original states formed on federal land.
Do it the same way things were done in the original states formed on federal land. yep, make em homestead it like everyone else. Or patent it under 1866 mining law, etc., etc.