NavList:

Eric:

The 0.1' discrepancy between the Almanac's correction tables and the other results is more an artifact of the design of the table itself rather than its underlying theory.  The lower half of the tables are basically "average" corrections for that particular column's apparent altitudes, and 80° just happens to be one of the endpoints of its particular column.  Try comparing your results for an apparent altitude of 82°30' and see if it persists.

I personally don't have a copy of (what I presume is) a recent copy of Norie's Tables, so someone else will have to confirm results there, but more broadly there's "differences in theory" and then there's "computational blunder."  Bugs in spreadsheets happen, and you're deliberately looking at an extreme corner of the table where most users haven't had cause to look at during day-to-day operations.  It also happens to be an altitude that's difficult to measure with a sextant and an intercept that's tricky to plot on a chart, so such a small error likely won't be noticed against all the larger potential errors in drawing such a line of position.

The theory underlying parallax and augmentation is the geometry of straight lines and plane triangles and has nothing to do with the curved rays produced by refraction.  In fact, by pushing everything towards a common point (your zenith), refraction actually works to reduce the moon's apparent semidiameter (by amounts entirely too small to measure with a sextant when the moon's altitude is that high).  The proper "order of corrections" is dip, then refraction, then parallax and augmentation.