Looking for a more elegant solution than rolling more dice...

If you want to go a less-predicatable route than that above, have a deck of micro-size cards, each with a different number on them.

You can reshuffle the cards to restart or when the discard is exhausted, or you can shuffle the discard and place it back on top of the draw deck to simulate that repaired locations are fragile after being damaged and then patched-up again.

You could do the same thing with a pile of chips face-down, or chits in a bag or other container. The underlying concept is the same.

This would be the same card dynamic as you see in Pandemic, so if you're familiar with that game then you will understand what I mean. Instead of cities across the world, it would be rooms within the starship.

Have you tried to limit the game because of the dice?
The rooms are color coded, so how about a maximum of six rooms per color on a ship? That'd make randomization a breeze.

Give the game board a subtle grid overlay or assign a grid designator (A1, B3, C5, etc.) to each room on the ship.

For 18 locations, use a d6 (A,A,B,B,C,C) and another d6 (1-6). Every turn, roll both dice to determine the current room with a crisis.

Will it always be the same starting 6 rooms that can have the initial crisis?

If so, it'd be easy to make 3 section dice; green, yellow, red that escalate as the game progresses. Green (A,A,A,A,A,A) has the starting section of rooms only. Yellow (A,B,A,B,A,B) branches out to another section of rooms. Red (A,B,C,A,B,C) includes the entire ship.

have you thought about trying for a different theme? "Crew of a starship" is already a pretty well-occupied niche, with Stronghold's SPACE CADETS, CGE's SPACE ALERT and the new Mayfair game FIVE YEAR MISSION. Finding another theme that's similar but slightly different might help your game stand out, and it might also give you some thematic input into the randomization problem.

Just a thought.

Integrate the new crisis location into one of your existing decks of cards instead of making a new deck. Add a colored icon to indicate the location's category (yellow=engineering, orange=cargo bay, etc.) and also add a cardinal direction to indicate which room within that category. You can use port, starboard, fore, and aft to be more thematic. To break ties (say more than one engineering room is farthest port) you could assign a priority value to each room card in a category. On the crisis card indicate > or <. For example: Crisis- Vole Infestation. Until Vole Infestation is resolved, make a crisis draw each turn. (<) blah blah blah whatever negative thing aninfestation does.

Draw the top card from whatever other deck you put the icons on. It's a yellow port icon, so the voles infested the leftmost cargo hold and the one with a lower priority value if two or more rooms are furthest left.

If you use 2d6 and number your locations as follows you can have 21 total locations. This could drop to 15 if you then have rolling doubles grant some sort of alternate effect (perhaps something positive and you roll again)

1-1
1-2
1-3
1-4
1-5
1-6
2-2
2-3
2-4
2-5
2-6
3-3
3-4
3-5
3-6
4-4
4-5
4-6
5-5
5-6
6-6

First off after playing the game mansion of madness, I love games like this.

first though (unrelated to your question): have you thought about something like have different types of problems. if something goes wrong you flip the board over to show a new image with something different. If its something like fire, you are timed and it can spread to different rooms.

just an idea to help out.

Now lets see if we can solve the problem at hand. You dont want dice and you have too many cards. Im thinking a resource management puzzle eg you are given parts to repair or something and if you use it to repair, how much you use for one objective will greatly change the next objective. if you use too few parts, that room is likely to break again, if you use too much you might not have enough for the next goal.

now for how to choose the areas. welp this is proving more difficult than I though. Something to ponder though, instead of forcing the damage, why not think of it as punishing the players poor choices, eg they navigate into an astroid. so think about it from the perspective of the players not the environment. if that makes sense.

this sounds like a fun idea so I will keep thinking! good luck