Thanks for the responses!
Unfortunately, that's not really an option for me, since I use the hold function on the Recents button for multi-window. Ideally, the other options to take a screenshot (three-finger down swipe, power button menu, etc) should be updated to work on the TwinView screen.
Okay, for some reason, that wasn't working before. It's working now, though.
Having the TwinView connected forces things like the Recents list, web browsers, messengers, Gmail, etc into landscape with no option to rotate to portrait. Ideally, there should be an option to allow for forced portrait or auto-rotate when the TwinView, that way we can pick what works best for us (and I know not everyone's usage is gonna be the same as mine!).
That's a shame, because I think it looks cool, but I don't like having to take off my case to use the TwinView. And as mentioned before, for some strange reason, Asus designed two different Aero Cases for the phone, and the one that came with my phone covers the air vent.