I finally found a solution in one of these posts. It seems totally random and completely unrelated, but it *did* allow me to actually sign in!
There is a bug in Apple TV app causing this problem and rebooting the roku/reloading the app won't help. Sure it may help some, but many people have reported issues with the Apple TV app where most programs won't play but a random select few do.
This problem has existed for many months and why both Roku and Apple fail to acknowledge it is a mystery.
A fix has been been posted to change the HDMI audio setting. Roku has changed the menu structure so the previously posted directions can't be followed. To make the change using the new menu:
Settings —> Audio —> Digital output format —> Custom —> Dolby
