Then perhaps the clearest way would be to have an explicit switch, perhaps called "Presenter Mode" that would do it, rather than bundle this extra feature into another mode change, which some people might not want to do, for example if they want to change/correct a lyric on the fly, or put up an announcement, or something else that's disabled in viewer mode, and so not want to switch between viewer/edit mode. It would also be more user-friendly, I think.
(And I found Shift/PgUp and Shift/PgDown also scrolls page by page in the areas I tested.)