I don't see a lot of harm in allowing JD to go to Columbus and start work now. Yes, he will have a "playbook" on the Rangers, but ostensibly one of the reasons for his firing was that Dolan wanted something of a different playbook. He may have insight into the draft board, but is our draft board finished at this point? It's two months away so probably not, and where we're picking can totally change our strategy. As we've seen, Gordie has taken a step back to some degree, and there will likely be some different voices in the war room, or some of the same voices amplified a bit.
Even if JD did have some type of information that he could use to leverage against the Rangers and put them in a really difficult spot, I doubt that he would. He's the consummate "good guy" in the league and wouldn't go out there trying to f*** his friend and protégé Drury right when Drury's getting started.
Doesn't seem like JD leaving and starting work now is much of a threat in any way, IMO.