If you can rip out the old motor and tie a string to the door (drill a hole in the piece that moves?), you can get a standalone motor from chicken guard. (You’d want the pro model or cheaper; their new all-in-one would have you replace the old door)
I might do this, but the servo still works. So long as I can still drive the servo, I think I'm good. It's open loop, so I'll need to watch something to determine when the door is fully shut.