Suggest you use the status line where you show the page number (i.e. 1, 2, 3, etc.):
When I tap the digit "1" on the status line a small popup "navigation" menu occurs, it has few touch-buttons:
(1) "Jump" to leftmost margin top paper edge (2) Jump to rightmost margin top paper edge
(3) Jump to mid-page leftmost margin (4) Jump to mid-page rightmost margin
(5) Jump to leftmost margin bottom paper edge (6) Jump to rightmost margin bottom paper edge
(7) stay on same line jump to leftmost margin (8) stay on same line jump to rightmost margin.
The idea is that the user with 2 quick consecutive taps can position the virtual large page to any specific position of hers/his preference.