Thanks again for rechecking, and good catch! On its last day, an order now says in red "🌙 last day: leaves tonight", right on the note, so it's clear the client won't wait another day. It's live in update 0.7.10.
And thanks for the note on the coin flip: paying both rents by day 6 is the expected pace. The flip usually shows up later, once you dig deeper and the rent goes up with depth.