He doesn't really have to do anything proactive to clear his name. The arrest of JMK and Mary Lacy "clearing" the Ramseys in 2008 did a lot to sway public opinion about the case. Since Patsy's death, John's done interviews on Oprah, Larry King Live, 48 Hours, and some local news station. In all of those interviews, the 'theme' was that John was 100% innocent and had been vilified by the media and the public, not that he was trying to prove to an audience that he was innocent. I'm sure that John would only agree to make appearances on shows that agreed to paint him in a 100% positive light.
Also, John's book is coming out next year and I'm sure he'll be doing some interviews to promote it. I can guarantee that any interview he does will not ask him, "Did you kill your daughter, JonBenet?" but instead will ask "What was it like being blamed for your daughter's murder when you and your wife were innocent?" Perhaps by taking interviews where it's 100% IDI is John's way of clearing his name by changing people's thinking about the case.