I think this is neat!
I have no answer but I want to help the post gain attention by putting a comment in here.
I would be super interested in the answer as well, though again I have no idea what it might be or even what factors go in to the equation. I may be off in my assumption (and you may have already accounted for it) but I imagine the calculations for a satellite orbiting the body whose horizon is the subject must be different by at least one term from the calculations of governing a body orbiting the same mass as the horizon-owning-body