Mechs can be repaired , it takes time and resources. The dungeon crawl needs to be changed to meet Alpha Strike's repairs. (Or AS changed to allow faster "healing", but I'm going to go wth changing the dungeon.
Make the world a dungeon. You need to find the location of the quest object (raid on command, computer center?).
Then you need to find a way to the object, maybe some recon raids.
Then you need to bust through a guard room ( assault).
No time for any repairs now as they rush for the object.
And finally fight their way out again.
Use the chaos campaign to track repairs, they only have so many war chest points for repairs before the mission is scrapped as a lost cause, until they are in the middle of the crawl where there is no time for repair any way.
Some repairs might even be too lengthy (engines?), so they can fix armor in time for next mission, but have to leave some crit damage if they want to achieve the objective.
Or a "crawl" where they are on the run, trying to survive until reinforcements arrive. They have limited families and supplies, achieving additional facalities/supplies must be compared to the risk of taking them.