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Andrew:

Regarding your first question about the choice to round-then-difference rather than difference-than-round, in the case of these specific tables, where the position of the moon is

• tabulated hourly
• to the nearest 0.1'

then the only real advantage to the almanac offices' choice to round-then-difference is that it saves processor cycles.  However, there's also no compelling reason for them to change to a difference-then-round system.  The rounding errors are moved around, but can't be reduced overall.  And don't forget that the intended use of these numbers is with an interpolation table that rounds to the nearest odd multiple of 30 s.

If you really wanted to be fancy, the USNO has a history of tabluating the first differentials rather than first differences, to aid in calculating the effects of second differences for some data, but that's not warranted in an hourly ephemeris of the moon tabulated to the nearest 0.1' (which is by design, I believe).

An aside:  the included instructions for the Air Almanac specifically tell the users to round all values for the sun and stars down to the smallest integer rather than to the nearest, with a note towards the end suggesting rounding to the nearest 1' for added precision.  There's also several pages dedicated to exploring the effects of different kinds of roundings on calculating local rise/set times