You have a map of the ship, with rooms and doors. The game is simply a lot of fetch quests. Get the wrench from the repair room and use it to open the fridge in the kitchen. Get the spare battery from the living room and go to the generator room to install it. You'll be doing these quests simultaneously, so you can do things like go to the generator room to install a battery, find the blueprint lying in the corner, and write down the rogue AI emergency shutdown code (all at once with one visit to the generator room).
So the goal is to go from room to room doing this, and get everything done, traveling between rooms as little as possible to get things done as quickly as possible. That would be where the time limit comes into play, although you could maybe turn it into a high score, and it could be a number of rooms traveled to (probably easier to just implement a time limit, and you could have some doors open more slowly than others.)
Maybe you can add something about ventilation, being only able to ventilate 5 rooms at a time and there being a challenge to switch the rooms being ventilated, as infrequently as possible.
https://www.youtube.com/watch?v=4pir754VfNQThis could be a copy of Diner Dash? If you can't make the above idea work.