I am going to be sore tomorrow. Put my new fan in today, but I still need to replace the outside wall cap. Maybe next weekend. Here's the old fan, at least I'm pretty sure a bona fide electrician installed it:
The new fan is a TIGHT fit.
Also found a little surprise. At the wall cap, there should be a section of metal duct through the wall that the plastic duct attaches to. There was not, instead the plastic duct was just kind of shoved up against the inside of the cap. So here is my temporary solution, a bunch of foil tape.