Yeah I was considering how to repair it. The part that broke was the bottom of the little hole. I was thinking it might be able to bend a little piece of metal so that the door will catch on the rotating part, but the space is so tight to work in and I have such giant meat paws that I'd have to take the housing out to fix it anyway.
Side note: I'm not 100% that a mechanic broke it, honestly. The motor has basically a little plastic nub that rotates the door. It seems like a lot of stress on that part (relatively speaking), so it's possible the plastic just cracks and gives out over time, especially depending on the temp/humidity/etc being applied to that plastic on a regular basis.
It would be awesome if someone figured out how to 3D print a repair for this. It's probably $0.10 in plastic (at least for my issue) to print some sort of insert that would mesh with the motor "nub" and just glue onto the remaining part of the recirc door. I'd gladly pay $50 or more for a (probably) permanent fix like that.
BTW the blower assembly removal (which includes the recirc door) is a 2 step process

It's the AC removal in step 1a that has 18 subparts more complicated than an annual Ferrari engine out service

Seriously, why do you need to drain the entire AC system to replace the blower assembly?
View attachment 2575594