Sorry I won't be of much help to you, but...
I contacted the Collegiate Licensing Corporation (CLC) in Atlanta and followed their steps. It's easy to follow. They did their market analysis for my idea, they didn't think there would be a large enough market
, so I put it on the back burner. I didn't try any of the pro sports, but hear you need a team of lawyers to crack that egg. So, I would suggest the CLC as a first step.
Now for the info you didn't ask for and probably don't need:
If you receive positive feed back from their analysis and move forward, which I think you will, then know that there will be royalty fees for each of the universities. I believe they range between 5-10%.
I'd also start in the southeast for collegiate sports...not that you probably didn't know that already. One good way to crack the scene is to go directly to the booster clubs for advertising the product. Try to hit the fans in their home towns before they leave for the game.
Another thing I did prior to contacting the CLC, was go through a friend of a friend at Florida State University. She was a long time Seminole Sports Shop owner in town who now heads FSU's licensing department. She knew the ins & outs and was able to provide me with some guidance as well. Sorry, I don't have her contact info handy.
Every team has a website with forums similar to this for sports discussions. I'd pay the membership (Rival.com is a very good one), create a user account and screen name under your business, put a link to your website and photo of your product in your signature. Every time you post, you're advertising. Have friends post for you, but make sure they're representing the company well. That, in my opinion, is a great way to advertise cheaply to rabid fans and tailgaters. You can also do a market analysis of your own in a way by gauging the response you receive.
Also, and I'm sure you've already done this, but there are websites devoted to tailgaters you may want to check out. You can advertise there.
Sorry I didn't make it further through the licensing process, but I would suggest looking at the CLC first.