When I play solo, sometimes I like to wait for the right gate to pop up on the television screen before changing levels.
It would be great if when you look at the Gate Map and hover over the next set of locations, it shows how many minutes remain before that gate pops up on the television screen.
That way if you know you have 6min you can go grab a water or something while you wait. :P
For a newbie it's easy to miss the fact that there's any rotation at all. Showing the time somewhere, as you suggest, could be one way to hint that things change.