> A few months ago a few keys of the keyboard stopped working, specifically the 5, 6, -, = and Delete keys. Sometimes I can get it working again by mashing one of them for a while, but it's not consistent.

I had the same problem on my X1 Carbon generation 6 and managed to fix it simply by disconnecting and reconnecting the keyboard ribbon cable. It's a very easy fix, the only thing you have to unscrew is the bottom cover.

I may be wrong here but IIRC at least with the 7th generation you have to disassemble the whole thing to get to the keyboard. I'll have to take a look though, because if it's really that simple then I may be able to make my life a bit easier. Thanks for the suggestion :)