That math is quite helpful... and slightly painful.
I'm still leaning towards keeping that number on the low side, to keep those "We're the only ship in the <insert unit of measure here>" far more plausible. But, perhaps upping my estimates by, say, 50% are in order.
For those interested, I have also begun some revisions to this historic section of the writeup which I may post soon. The technical section is of course highly contingent on what the "real" size of the ship finally ends up being over in the other thread.