In general, an "out of the box" 3 tier solution for sitting is probably impossible, but that doesn't mean it's un-doable. With the right keyboards, I think a K&M 18880/18881/18882 combo would do it with some pretty minor modifications to the stand (having done something similar). There is also a company that makes nice custom stands that are not prohibitively expensive (or I expect would not be for someone who has the kinds of keys you do). There's also the possibility of using a combination of stands, like a low single tier stand in front of a double-tier stand. I play standing, but I've dealt with the same challenges creating stacks of 4 boards where I can reach everything, and I have found numerous combinations that have worked. But the choice of boards matters.
So that said, I think it's almost certainly impossible for you to do what you want with the 3 keyboards you mention, at least if you need access to their control surfaces, because of how big the boards are. The closest thing I could envision that might work would be some kind of custom setup that would put each board on rails, so you can pull one out when you need to access its control surface, then slide it back in for performance, and even that assumes you don't need to access all the control surfaces while actually playing. And it would have to be pretty heavy duty, considering the weights involved.
