I don't think this is possible. If you zoom out in the galaxy map you can't really see individual stars. The star density is just way too high. I mean I am sure the stars in the chamber map probably represent individual specific stars, but I don't see how we could possibly do a matching overlay to identify individual stars.
Unfortunately away from computer at this time.....but what happens to the view of our galaxy as we apply different filters to it and zoom all the way out? I've never applied filters and zoomed very far out, since I use the filters for "more local travel". Does the galmap still look basically the same, or does it more closely resemble the star map in the chamber? Not sure which/how many filters to apply, but if adding filters actually removes systems in the galmap when it's zoomed all the way out might give a resultant map that looks like the one in the chamber.