Rather than modifying the 'watch' command, use screen!
For example, let's say that you need to be able to see 300 lines of height and 100 characters of width and move around that. After starting screen, force the size thus:
C-a :height -w 300C-a :width -w 100
Now start your watch command. You can then use C-a <ESC>
to page around the display.
Unfortunately, the display doesn't refresh while in copy mode. But if you want to adjust which section of the window you're viewing, the easiest way may be to rerun the height/width commands as by default your terminal shows the lower-right of the virtual window.