I still think the best would be to combine the NIT and the NCAA. As I would do it, NCAA would limited (as it used to be) to conference champs. Winner is deemed "national champion." (Don't win your conference, you're can't get the "national" championship.) NIT is expanded to the next best 64 or 68. Winner of that tournament is deemed "NIT champ." The winners of the two tournaments play each other (maybe on the home court of the "national champion") for the "tournament championship."
I would go a step further and make the NIT brackets truly geographic (all B1G teams play in the Midwest bracket, for example) to keep interest in early games high (Loyola v. Michigan in the first round, anyone?) and burden on athletes low, and make things like "Midwest Champion" sort of meaningful.