So here is the pan I posted about a couple days ago. I put the pan in the oven and ran the self-cleaning cycle. When it came out I cleaned off the ash and I could actually tell that some of the texture around the edge was the metal and not food. The rest of the gunk was gone.
I put a very thin layer of canola oil on it and baked it at 450 for an hour. It looks beautiful now. I’m going to do a couple more seasoning cycles and then try to maintain it.
Thanks everyone for the advice!
Why would it damage the oven?
Apparently a lot of components aren't designed to run sustaining the 1000° F temps. https://www.familyhandyman.com/article/dont-use-your-ovens-self-cleaning-feature/
It can damage the oven, as well as the cast iron.
https://campfiresandcastiron.com/cleaning-cast-iron-in-a-self-cleaning-oven-dont-risk-it/#Why_You_Shouldnt_Clean_Cast_Iron_In_A_Self-Cleaning_Oven
This makes no sense to me and I would like to see some scientific research. We are not even close to the annealing temperature of cast iron (1300F-1400F). In no way can i imagine that a 1000F alone will make the pan warp. It really shouldn't be possible from a material science perspective.
What makes cast iron crack and warp could be rapid temperature change if you put it immediately under cold water after high temperature since the temperature gradient in the material will form stresses that could cause cracks. But if a 1000F warps the pan I'd say that it is poor quality cast iron or something else is going on.
My oven no longer works properly after the last self clean. The preheat cycle doesn’t stop at the designated temp — it just keeps getting hotter and hotter until it shuts down with an error.
I think self clean is quite bad for the electronics in the oven. Electrolytic capacitors are an example of one type of component that gets damaged over time by heat: the electrolytes dry out and the capacitor fails.