So would the wood chips be some weird part of his signature, or just sloppiness?
The three pieces of evidence that have been mentioned - the DNA, the incriminating comments JB made when picked up, and the wood chips - I'm hoping there's more, as I can see a defense lawyer putting on a good show with just that. And JB's attorney has said, in order, that "sex isn't murder", that he hadn't been aware that JB had said anything to LE before he was on the case (we hope the Miranda part was taken care of correctly), and that there's thousands of carpenters.
Speaking of Bittrolff's attorney, he certainly got himself the right attorney, and he must be pricey (who's paying?).
William Keahon doesn't just have the bona fides (Chief of Homicide with the Suffolk DA's office before founding his private practice), but he's also defended exactly this kind of case before (still, as per that link to his home page, there's apparently no level of professional accomplishment that ensures you'll get your copy proofread. Just a peeve of mine, look at the second sentence here: "His cases range from high profile white collar crimes to murder trials and everything in between. To attempt to reference or name them all would be futile, if he is not on trial he is preparing for another one." First, it's a semi-colon needed there, not a comma, but more importantly I don't think Mr. Keahon is actually ever "on trial". Sentence should read, "To attempt to reference or name them all would be futile: when he's not at a trial, he's preparing for one". Anyway...).
This 2009 Newsday article notes that Keahon is one of Long Island's most prominent defense attorney's and has represented, among others, serial killer Robert Shulman, and Evan Marshall, who beheaded a retired teacher. Keahon tried to claim that
Shulman, who bludgeoned and dismembered five prostitutes in the Hicksville area in the late 90's, had confessed under duress, and then suggested that it was Shulman's brother who really committed the crimes - those attempts both failed, and he died in prison in 2006 after being sentenced to life.
Marshall, a sicko of the worst order, in 2007 beheaded and dismembered his victim and stored the parts in his parent's Glen Cove home, where he also lived. Keahon tried to claim that his client couldn't have put the body parts there because he didn't really live there; the police produced a driver's license where Marshall used his parents address. So Keahon then tried to claim that there was no photographs or proper logs of the police finding the body parts at the parents address. That ploy failed as well, and Marshall received a term of 30 years.