I would have just let the blame for the crimes Harvey committed settle on the Joker. No public statement of his, presuming he even denied it, would be believed. Batman, by taking that blame, has now made his mission wholly untenable. Cops don't forget certain things, and a supposed cop-killer tops that list. Hell, even if he were cleared the next day with credible evidence, there are some cops, particularly on an urban PD like Gotham's, who would never believe he didn't really do it. Part 3 will have to tell us if they can credibly salvage his ability to fight crime. Gordon, IMO, will not be able to control his people. He'll say one level of 'bring him in' and they will be thinking a very different one.