I don't know what Ulis' motives are, if he is doing it for money, fame or if he really wants to solve the case.
I have been following him for a while now and haven't been very impressed so far. His suspect Vince Peterson seems like some random, innocent guy who is now tied to the Cooper case forever. There is zero evidence that he has anything to do with it.
That being said, I do like Ulis' idea of searching for DNA traces on the spindle of the tie clip. It is worth a try imo.