Thanks for digging into this for me. Yes, both cases are necessary for typesetting shape note hymns, as illustrated by the attached scan. I believe the rule for this is that the notehead should be pointed up in the treble clef, and down in the bass clef.
Of the three hymnals that I have that use shaped notes, two do *not* reverse the Fa notehead in the treble clef—so Lilypond’s current output matches what those two hymnals do.
Since I primarily reference one of these hymnals for the engraving I do with Lilypond, I had never seen the behavior that you are describing until you pointed it out.
Now I’m wondering how representative those two hymnals are.
David
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