Hi Brian,
Interesting question. The first thing I wondered about was how the projection of the content was going to be played. Are each of the screens going to be played independently from a separate source or all from a single source? The answer to this would have an bearing on how you approached the project
If it was me, I would create one project with three separate sequences and then nest the additional sequences for reference (so you could see where each was at during playback) you could create some kind of simple picture in picture for reference while editing and then just turn them off when you exported. I would probably only export the audio with one of them. From there it would just be a matter of starting playback of all three at the same time.
If they are all one long screen, same approach, but create a master sequence that is 3 times the width. See the second screen shot. I created a custom preset and manually changed the width.
It could be done in either Premiere Pro or After Effects, here are some visual examples of how it could be done.
(click to view larger)
Hope that helps,
-Dave