A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: David Iwancio
Date: 2021 Feb 14, 14:48 -0800
Your hunch is right: the issue is horizontal parallax.
Remember that the celestial horizon actually passes through the center of the earth, not through your eye. Figure 1429 in the 1984 edition of Bowditch (in the chapter on navigational astronomy) shows the difference, but it apparently got replaced in later editions.
If you flip to the back of the Nautical Almanac, to the moon correction tables, you'll see that when the moon's upper limb is on the visibile horizon (apparent altitude of 0.0') and its HP is 57.0', the center of the moon is actually still 7.6' (34.5' - 30.0' + 3.1') above the celestial horizon. If your bridge wing is high enough above the waterline you could still catch the moon's upper limb when the center is actually on the celestial horizon, but you're already in The Bad Place with regards to refraction. Going by the moon's upper limb on the visible horizon, regardless of height of eye, is a close enough approximation for compass checks.