I feel like a total idiot and should know better than to leave the extension on the floor behind my feet when working on the car. I accidentally kicked it and one of the studs got caught in the relief cut in the garage floor and broke the stud off.

Any way to fix this? Or do I have to buy a whole new housing now?

Drill it out and use a cut off bolt or threaded rod, works fine

Great idea!! I'm having one of those "Why didn't I think of that" moments right now :)
Thanks!