NavList:

Using your analogy of the moon as a "boat," by "perpendicular bisector" Letcher means a line that cuts that boat amidships, with equal parts of the crescent fore and aft.  That line will ultimately run through the sun, and the bulk of the moon's motion against the stars is along that line.  If that line is within 30° of your local vertical (n.b. your vertical circles are azimuth circles, which is where Letcher was going with that bit about azimuth), then your altitude sights will contain at least 83% (i.e. cos 30°) of the moon's orbital motion.

And you're also right about the "pitch" of the "boat" being different at different latitudes, at least when the moon is near the horizon.  Getting that 30° angle will be tougher at higher latitudes, as higher latitudes generally result in a higher "pitch" near the horizon.  Chances are more in your favor when the moon's declination is of the same name as your latitude and the sun's declnation is contrary.