I've been learning a lot watching you work through these text alignment problems over the last months. Thanks for these, and for the clarity of the writing as you've been developing the Lily code as you work!
I have no answer to the question at the end of your previous mail ("why does the combination of these three tweaks work?"). However, I wanted to mention that I've found -- finally -- a solution for baseline-aligned textual annotations that's been working for me in my own scores now for about a year: sticking all the text in a text spanner with invisible line segments between each element in the spanner.
I remember reading through a thread where this text spanner approach for vertical alignment came up, and I remember you had good reasons for continuing to work with individual TextScript objects instead. But I just wanted to pipe up and add that after years of going the text-script-with-staff-padding route (and never getting 100% "stable" results in the vertical positioning), that switching last year to the text-spanner-with-invisible-segments route has finally yielded a solution that seems genuinely stable.
For years, the missing piece had been that Lily didn't allow multiple overlapping text spanners in a single voice; that's a nonstarter in much (probably most) recent music, of course. But then David Nalesnik provided a solution, all the way back in 2015:
I now have a bunch of custom spanner definitions using David's alternateTextSpannerEngraver, which implements spanner-id, allowing for layered spanners. David's alternateTextSpannerEngraver should *absolutely* be included by default in Lily; I'll write that to the appropriate thread in a bit. At any rate, output like this now works consistently for me, for the first time in 13 years of using Lily:
(The fractions show "bow contact points": 0 for talon; 1 for point; 1/2 for midway up the bow; etc. The T and P are tasto and ponticello, as you'd expect.)
So, even though that example draws the text spanner line segments in a visible way (dashed or solid), you can easily imagine setting dash-fraction to 0 to make segments invisible, leaving markup aligned in the correct way.
Ok, that's it; I know you're elaborating the text-script-with-staff-padding way of working. But just wanted to attest that the text spanner way does seem to be a viable alternative if you later become interested in that way of working, too.
Trevor.