I unfortunately cannot help with the servo hat question, but I would LOVE to see the "iris" and actuation mechanism you are using. I've wanted to do exactly what you suggest with a fan on my enclosure (i.e., close it off when fan not running) but have not found any good iris or louver system I could easily adapt.
Just printing the bits now to see how well it works, currently my plan is to use home assistant as i can trigger the python script once a set temperature has been reached