Sounds good to me! You would probably have to pay the x percent or whatever cash advance fee, and the 1 percent Traveler's Check fee - and -- -- Well, maybe this isn't such a good idea after all. I see fees approaching $1200 for the $30,000 tuition, which does not sound like such a great deal.
One of our son's schools (UVM) did not accept credit cards, but switched over in his senior year, and our last son's school (College of NJ (formally Trenton State)) did not accept cards for his Freshman year, but did for his 2nd and 3d year, so keep on asking. Obviously, you have to immediately pay off the card when you get the bill so you won't get socked by the interest charges.
Keep on trying!