You couldn't find a variation that would make it work because it seems that there is none. The complete list of options related to the chord naming should be on this page in docs: https://lilypond.org/doc/v2.22/Documentation/notation/displaying-chords .
It looks like you will need to set the
chordNameExceptions. There is a snippet in the snippet list that does a similar thing and that you will probably be able to easily adapt to whatever you need. Have a look at this lilybin (a web app that compiles and renders Lilypond snippets).
(By the way, I'm not sure why you set the major 7 symbol to maj9 and want to set the half diminished symbol to m7b9. If you want the 9th chords, then it will be far cleaner to write them as such, for instance with
d:maj9. And if you use e. g.
c:m7.9- for your m7b9, then an appropriate symbol will be used so you don't need to change anything.)