If you haven't tried Screen Sharing since they deprecated VNC and switched to their proprietary H.264-based protocol, its worth trying. Even YouTube videos play just fine with no noticeable lag.
It worked relatively well, but wasn't perfect. It was as close to what you're describing as I've seen, though. This was a few years ago; something like this might work even better now.
Unfortunately, it relied on Display PostScript and Quartz née Display PDF isn't architected to allow that sort of remote display/access on a per application level.
It’s pretty good.
To be clear, it’s not ever supposed to be a primary. It just becomes one from time to time when I make it full screen and am not paying attention.