I had an oven that did this. The self-cleaning latch would latch as if driven by a culinary poltergeist and there you were. It did other annoying stuff too and there was an error # that would show up. Sometimes unplugging it or turning off the circuit breaker would work. There was also something that the repair guy showed me where he'd start the cleaning cycle and then do...something...and get the door to open. The same guy also jury-rigged it for me while waiting for the part to come in so I could use it. It was quite the saga: first dealing with A&E factory service who would call and say they were coming when I couldn't be there, then repair guy#1 who ordered the part, then repair guy#2 who came to install it and said it was the wrong part and ordered a different one, then repair guy#1 who said the second part was the wrong one and ordered the right one again and then repair guy#3 who finally installed it. Each time dealing with the inept A&E dispatchers. I swore that I would replace the oven the next time it started to act up and did. It was a Jenn-Air, which was bought by someone else.
New oven was purchased from a local business that also does repairs. The person that owns it lives down the street so I figure I'll go knock on his door and ask to use his oven if this one ever runs amok.
In defense of the OP, my favorite cookbook is called Roasting, by Barbara Kafka. I often cook everything at 500 degrees. Fish, veggies, beef, turkey. The outside gets crisp, the inside stays juicy. You just have to be very very careful to watch your time. Fish, for instance, is 10-15 min. A turkey (15lbs) takes about two hours, unstuffed.
I have the same stove/oven as the OP. Guess I'll see where the circuit breaker is before I cook again.
There is no snooze button on a cat that wants breakfast.