Okay, so off the bat you will see the same constellations as the London example. You have to imagine that NY has moved 12 hours away from the sun at Solar noon. So on the map, at 12am solar time, NYC will be positioned between Draco and Bootes and near the Bering Straight around 180 longitude.
I'm diggin' your map, I'm just unclear how one might use it, functionally. I think I get your statement above, by the time Solar midnight has reached me in NYC (It's like 7AM in London) I now see what London was seeing at their midnight.
Back to my Polaris example, NYC, midnight, way over on the left side of the map, which way am I looking, on your map, when staring at Polaris above the horizon? I kinda feel like I'd be facing leftward on your map. If so, which way would a Londoner be looking/facing at Polaris at the same time I am? Eastward, to the left, like me?
Here's something kinda cool you might like, old school:
The In-The-Sky.org Star Wheel