Aside from some of the names you mentioned, the first person to come to mind was Eric Tucker, from Bedlam theatre. His lack of Broadway credits is maybe self-explanatory, given the kind of work the company is known for -- but he's definitely been a fixture of the Off-Broadway scene for over a decade.
In that same vein, you could throw the Fiasco Theatre folks in there too (Ben Steinfeld*, Noah Brody, et al).
I also thought of Oskar Eustis* -- he's not necessarily all that acclaimed as a director, but he's certainly a director who is also an incredibly important figure.
As far as directors who haven't necessarily gotten a lot of individualized attention, but who are well-established in the NYC theatre scene, we also have: Lee Sunday Evans and Chay Yew.
Eric Ting has been directing regionally for a long time, but I didn't know about him until some of his recent NYC credits -- which I've been very impressed with on the whole. Definitely on my radar!
*(both of these guys have Broadway credits, but neither as a director)