Here's my idea:
A college scholarship is adequate compensation for 95% of college athletes. It's the 5% that in a free market would demand leaps and bounds above the scholarship compensation. However, I think everyone is aware of the impact title IX can have on this, so you can't just compensate some instead of others.
The only way to get around Title IX and to prevent college athletics from turning into a bidding war is to allow players to profit off their own likeness. There would have to be a cap put on yearly earnings though, that is the same for each player regardless of gender or sport. Just to prevent a car dealership from giving a college freshman a million bucks for appearing in one ad. What number that cap would be could be debated. 25,000 a year? 50,000? Obviously this would have to be closely monitored, which is why I think you allow the University to have complete control over setting up endorsements, selling autographs, memorabilia, etc, for the players. The university could even get a percentage cut.
The only flaw I can think of with this system is there would have to be swift punishment from the NCAA for violations, which let's be honest the NCAA doesn't do a very diligent job of that at all unless you decide to trade memorabilia for tattoos.