If you could do that, it *might* be possible to get a clue as to what is causing it (or at least increasing the chance to happen over vanilla).
Even so I can't make any promises for a quick fix yet. If you just want to get on with your campaign I understand, and doing so via console command is probably your best bet right now.
Thank you so much for the feedback!
I am quite happy to hear it's been challenging, because for me it felt like the game is easier with XLRP, if anything. That being said, if you have Better AI installed it'll make a difference. The only thing about Better AI I don't like is the extreme tendency of the AI to delay its turn. It will often just sit there and wait so it can react on your actions. It can get little annoying to be honest.
If any of the following standard parts is destroyed, clicking "confirm" twice when the repair time/cost window pops up should replace them for you:
Std Engine
Standard Gyro
E-Cooling
XL Engines, Gyro Mods and E-Cooling+ are lost like other weapons and gear and need to be replaced. Also, fusion cores can also be lost on Mech destruction and will need replacement. Getting the right replacement core in particular can be hard for some Mechs, and buying a new one is rather expensive. So don't worry if you find yourself putting a way larger or smaller engine in a salvaged Mech - that's pretty much normal business for Mercs (unless you are 1) filthy rich 2) far into the game or 3) are playing without Adjusted Mech Assembly or "unequipped Mechs" option enabled).
EDIT: Judging from your screenshots you're lucky - the components, including the 240-rated fusion core, are merely damaged and can be repaired. Otherwise you would've had to install a new core first.