Like either side will listen to me, but here it is, and it will work:

Compromise, part 1: NCAA takes a page from girls' soccer at the middle and high school levels, played outdoors, in variable weather conditions. So: the uniform rules are expanded to include a certain range of acceptable optional clothing to be worn under the uniforms. Long sleeves and long pants of tightly specified design may be worn as long as they don't inhibit any safety equipment, and as long as they are the correct colors to accompany the uniform colors, which will be stipulated by the team, to avoid confusion on the field.

Compromise, part 2: Imam at the young woman's mosque sanctions a symbolic piece of headgear for use on the field, court, or what have you. It can be very small, as are the little caps the Mennonite girls wear (locally called "sin sifters" because they are made of tulle, a fabric which resembles a sieve). This will provide the proper sense of modest covering in a symbolic way, while not exposing the player to any undue hazard involved in wearing a garment for which the sport is not designed to accomodate.

I like your idea about making an attack on the headgear carry a very stiff penalty. It would be a target no matter how large or small it was, especially if the attacker had a thing against Muslims.