Electrical outlet installed by previous owner had Black and Green wires wired together
I ended up putting it back the way it was wired when I opened it all up, just with new outlets. I think I'm supposed to put this info in a comment, but I can't see an easy way to add the requested images to comments.



This is the first socket I opened. In this pic I have it wired to the new outlet. My wife tells me that the wire I assumed was green is actually dark gray. (I'm mildly color blind.) When wired like this, the outlet works, but the second outlet does not.



Here is the second outlet (original) pulled out.



Inside the second box there's a black and red wire twisted together. I'm not sure where the red goes. There is an outlet above the stove that the range hood is plugged into. And another outlet for the gas stove. Neither of these two outlets were affected during this. They are not on the same circuit breaker.
At some point in the house's history the stove was switched from electric to gas. So I'm not sure if the outlet for the stove was added then or what.

In the end, I went with the "if it ain't broke, don't fix it" approach.