So the way that I've ruled these Part Breaks ((Which will deffo be on the page that talks about Empty Part Slots)) is as follows:
When taking an Extra Part you must mark that Part as being attached to the Core. When Rolling a Part Break do so as normal, Extra Parts only become part of the equation if the Core is rolled. IF the Core IS rolled and Broken /all/ Extra Parts attached to it become inaccessible / unusable until Pilots perform a Repair.
For an even Scrappier Game: When the Part attached to an Extra Part breaks have the Pilot Call Evens or Odds for each Extra Part. If they are wrong the Extra Part also Breaks. If they're right it merely becomes inaccessible as described above.
While a bit punishing taking extra parts is incredibly powerful, so this feels like a fair trade-off. Breaks are supposed to really hurt when they start to go through putting Pilots into a potential death spiral, so losing access to all the Extra Gear you were able to bring makes sense to me.