[2] shows the helicopter taking off 2 miles away from the old saudi embassy in McLean marked “permanently closed” on google maps. (The current embassy is in DC proper, directly across the river from DCA airport)

I don’t think thats strong evidence that it took off from the old Saudi Embassy - thats pretty far away even given your caveat about accuracy.

Edit: it looks to me like the black hawk was coming from somewhere else with its ADS-B turned off entirely, and then turned on ADS-B once it reached the potomac to approach DCA. The first two datapoints of that flight already show it going 110mph, which its unlikely to be able to accelerate to in just 0.2miles after take off.

Edit 2: The route also looks very similar to this flight from 11 days earlier (but reversed in direction): https://www.flightaware.com/live/flight/PAT25 This shows the Blackhawk at 300 feet passing by DCA on what seems like a routine or training flight? I don't know how to look up historical flights to see if this is a commonly-flown route. On that flight, the Black Hawk flew past DCA at 300 feet of altitude, and the last FlightAware data for the American Eagle passenger flight showed 400 feet of altitude.