Why did you decide to model the damage to these systems in the way you did?
As far as I can tell, it's the only slot type where its absence is a reason for a game effect, rather than its presence.
Guns, let you fire when they are there.
Crew, give you dice to use when they are there.
Armour, increase your armour values when they are there.
Engine, give you MP when they are there.
Tesla Coils, give you a breach roll modifier when they are not there.
Could I suggest that each ship gets a Fire Modifier which is normally a negative equal to the number of Trim Tanks the ship has, and each Trim Tank gives a +1 modifier.
Yah, that's complicated. But is it more complicated than keeping track of which empty slots used to contain Tesla Coils?