Instead of holding your hand while playing with this information by turning it in some kind of gameshow-like countdown, how bad would it be if the game gave simply no timing information at all?
Just a description of being ‘stable for a limited time’ in the filament should be enough.
Players figure out it’s 20 minutes. Players keep track of their own time.
I think that would fit EVE far more than some UI countdown. Give some more responsibility to the players, don’t show them when and which buttons they need to click now.
Or if a countdown should be shown the last minute I much prefer a visual destabilization effect over a UI timer.
Let the universe feel like it is about to collapse, not the UI.