One way to give a hint is to bump the menu a few pixels inside the screen each time the mode switch button is pressed (a smooth animation but not more than 1 second, only in and quickly out, to not disturb when pushing it was the real goal). That way, it becomes known that there is "something" in the vicinity. Knowing the menu moves to the left to appear, and that it happen while pressing the mode button, is shouldn't involve too much tries before getting to it !

Also, the video mode could be added to the list. That way, if someone gets in the menu, he can still go to video and is not blocked, if it was not clear for him that pushing it was the "correct" way to do.

My 0.02€...

PS: By the way your application looks good, I only discovered it now !