I've also been thinking about a time-travel themed spin off to this idea. Imagine you were sent back in time some thousands of years, to a random location on Earth, and you had to communicate (via some fictional device) to a referee in the present day, telling them where you are, and
when you are, in order to be "rescued"/win.
Largely it would be the same challenge as the present day version, except you couldn't use vehicles (except riding horses/camels), and you'd have to navigate using only information that would have been visible at that time, like mountains, rivers, and long-lasting settlements.
To enforce this fiction, the players could receive information from a team mate that had access to a 3D model of their location as it would have looked in the relevant historic time period. That team mate would then be able to instruct them which direction to walk in, and which geographical features to follow.
Every night, players would try to observe the location of the moon and planets relative to constellations, in order to calculate which century, year, month and approximate day they are in. Of course, the players on the ground would know the answer, but would have to show how they worked it out, and their team mate would have to perform the same in a 3D model which uses a planetarium system for rendering the night sky of the intended period.
To accurately determine their location without cheating, the player on the ground would have to find their way to a location which existed at the time, and whose exact position is known in the present day, such as the Parthenon or Stone Henge.