I think the biggest reasonable compromise is to add some code that says that the ship will dock at a certain port in the sector at round end. Example: if we are in Elyra, the round end screen will say that it's about to dock at a port in Persepolis. This would allow people to abstract their free time away, it'd allow people to continue using the relay (off-time during refueling, cargo unloading or what have you) and it'd allow people to develop their character through discord DMs, while not killing the idea of a ship.
Additionally, this should come with a config option, so it can be disabled for a period of time if needed.