You will only be able to get coordinates for the portion of the galaxy that is hardcoded, the rest of the galaxy is a seeded number.
I see absolutely no reason why the CLIENT (or server if that is part of the network traffic on entering a system) can not tell us the coordinates for the nearest 20LY systems from whereever you are. It effectively have to know this already since it provides this to the target panel already. For the same reason I fail too see why the Client can not just provide coordinates in game since it is able to give us a 2 digit distance across the galaxy.
For mapping purposes, I could live with the distances to the closest systems, but it would make a commanders paperwork so much easier if the coords where provided. I'm afraid FD is overthinking this, a plain text dump when entering a system or visiting a market would be the simplest and most robust approach for 3rd party services.