Staples Business Solutions (which was recently acquired by Taylor Corporation), apparently has a solution that meets some/all of these requirements.
The downside is that the print production is very costly, and from what I've been told, the production quality and service is inconsistent at best.
Chasing it upstream, from what I understand, the Staples system is built on Four51's Order-Cloud platform.
To @John's point, there likely needs to be a programmatic or human review (or possibly both) of uploaded images to ensure sufficient resolution and brightness of the image.
@John, I'd love your thoughts about print color consistency, assuming @Kristi's templates have a defined color palate (possibly even a PMS spec), and they desire for that color to be consistent, print run after print run. I've found that the same printer with the same stock and the same art files will end up producing different results in different print runs. How do you mitigate that?