In case there is interest, what I did now was tweaking the Current_chord_text_engraver from scheme_engravers.scm. It simply takes the first pitch specified in a chord as the root, takes the first one with property "bass" as the bass, and it additionally listens to text-script-events from which it takes the first specified one as the suffix. I use that in a custom context called "HarmonicBackground" for lack of something better, same as ChordNames but with this engraver instead of the original one. For the input I just use relative mode.
chords = \relative {
<f \over ees>^"7"
des^"lyd"
}
\new HarmonicBackground { \chords
}
It's probably not foolproof; I'm a novice with both LilyPond and Scheme. Currently the text-script is hard-coded to go in the superscript of the chord, before the slash separator. Perhaps it would be nicer to look if the text-script is entered with ^ or _, and even nicer would be to use shorthands in an input mode such as the chord mode, but I didn't look at any of the input/parser code yet.
For myself that suffices for now; it looks good to me on the page and it's easy/flexible to enter.
If anyone more knowledgeable thinks it's worth continuing with, I'd be happy to discuss/help! (I can see several advantages and disadvantages.)
All the best, and thanks for the help,
Koen