New appliance time! The old one wasn't drying properly, even though it had been cleaned and the duct outside cleaned all the way through. Then it started running for only 10 minutes at a time. It is 15 years old, so we decided to buy a new one.
When it arrived, I was sent a message at work that the existing duct connector wasn't salvageable, so they wouldn't do the install -- fair enough. However, when I got home to do the installation, I turned it around and found this:
Kinda looks like it's been dropped.
Update: I called the customer service line, and a nice lady told me to complete the installation and if the dryer worked and we were willing to keep it, they'd refund us some money. So we'll run it over the weekend and see how that works.