Someone else mentioned the "Utes" could just change the spelling to "Yoots"... Just draw attention to the NCAA's complete idiocy.
I think the schools should make a positive out of a negative.
1) File a class-action lawsuit against the NCAA, not as individual schools but as a group of schools illegally singled out for discrimination. Let Alcorn State University(the Braves) be the lead plaintiff. Being a black school, it will be harder to tar them as insensitive to discrimination.
2) Hold a meeting of the affected shools and declare that they will henceforth hold athletic tournaments with each other in a celebration of Native American culture, the right to free speech and the right to free association. Optimally, this would be done during the time of the NCAA basketball tournament. They could probably get ESPN or FSN to buy television rights.
3) Agree that one of the major schools (Florida St. or Illinois) bite the bullet and decline a bid to the NCAA basketball tournament but let the NIT tournament know they will accept a bid there. Preferably a conference champion or a Top 10 team. Multiple teams would be even better.
4) Use money raised in Part 2 to compensate the loss of payout to stage the boycott in Part 3.
5) Point out at every turn that it is the NCAA that is practicing discrimination, not the schools.
This might achieve critical mass where we can force the NCAA into major changes instead of the schools.