Unfortunately I've already built all three of those reward buildings, so I'm not sure if I'd be able to run that test.
I'm a little confused about how you characterize the demand cap as a component of the issue. My understanding was that the demand cap is the entire issue. I think I've run out of most options for raising the demand cap (such as ploppables like the Major League Stadium), and I was under the impression that once you hit that point region play is the best bet for continuing to grow your city. Of course, I probably don't know much about how the demand cap actually works. Is it more fixed than I realize? Will providing more jobs (inside the city and outside) not impact it?
In any case, thank you very much for responding.