Really awesome, I may do something very similar to go on road trips with our dogs. We drove to Charleston a couple weekends ago (~3 hours) and our 4 dogs could have used a lot more room than what the backseat provides.
How long did you let it sit after installing? It's normal for the rears not to work while the unit is programmed by your specific vehicle. After you plug it in, you're supposed to do 2 sleep cycles and then let it sit for like 5 hours before it works 100%
You can black out your stock ones, which I think would look a lot better than flush mounts. I know that people want flush mounts for more than aesthetic reasons, but I think they will completely remove any personality from the rear of the truck.