I just got off the phone with Canon tech support, and they confirmed you can't use both a field monitor and the built-in display together, and there is no mechanism to control focus or anything else from the touch screen while an external monitor is connected.
However, I've found a not-ideal-but-still-functional workaround. If you use the Canon Camera Connect app on your phone and turn on live view, you'll be able to use it to tap-to-focus. The tricky part here is that, if you turn off servo AF so that you can use electronic manual focus, you won't be able to use the focus wheel of, say, the DJI Ronin S gimbal to control the focus anymore, as the camera will only respond to the Connect app, not the USB cable. You'll have to use the on-screen manual focus controls on the phone, tapping repeatedly to get it to continue to focus one way or the other. This also means having to mount your phone to your gimbal as well, which is just more adapters and weight.
This is frustrating, to be sure. It's easy enough to make it possible through a firmware update, but considering this has undoubtedly been discussed by other 6D owners, and Canon still hasn't seen fit to roll out such an update, it wasn't simply overlooked. It was intentionally left out. I've been a longtime Canon user, but more and more, Sony starts to look like a more customer-friendly company with their wares.
