Finally back with an update! It took longer than I thought because my wife's mother passed away and we had to devote a lot of energy to settling the estate (my wife is the executor) but I was finally able to complete this project, and we now once again have a working shade in our windshield! As we all know, AutoMotion doesn't want to support their customers with repair parts so an outside source for the motor is required. The source I found is:
RollerTrol Automation Systems
Motorized Window Blinds, Shades, Projector Screens, Skylights
They are located in British Columbia, Canada and the person I dealt with is the senior partner, Adrian Biffen. A great guy - he answered all my questions very promptly and was a great help. Anyway, they have a motor that matches the OEM specs exactly for $69, and they also have one with twice the lifting capacity for a mere $10 more. The motor part numbers are:
OEM equivalent: TMDC-12-25-07-34-NR
Higher capacity: TMDC-12-25-15-28-NR
They do require some work to adapt to the AutoMotion roller, but it turns out to be pretty straightforward. The project ended up costing me less than $100 - a lot better than having to buy a complete new shade! I decided to go with the stronger motor, figuring it wouldn't have to work as hard and might last longer than the original.
I've written up a tutorial that explains the whole procedure, and I'm going to attach it here. Hopefully it will help others who have had their AutoMotion shades quit working - if you have any questions, feel free to ask away!