The BLM typically publishes the locations of the five boundary points as part of the permit documents to determine the closure area, but the center point is irrelevant to them. DPW derives the center point from that, but they're usually to busy to publish it. Location of any of these major points might differ based on field conditions, accuracy of instruments, blablabla, and location of the streets and intersections as laid out might vary because DPW uses some pretty crude methods (tapes, chains, visual range finders, etc.).
So unless you know someone onsite with the time to respond to your query, or someone publishing their own interpreted plan of the city, you'll probably have to wait until you get there for something more-or-less accurate. Even if you knew the center point location, the as-built street layout might differ from what you might expect, and what you might get from some third party might be pretty inaccurate.