Chasing information and guesses about ancient modes

Suzanne Haïk-Vantoura makes the comment that it takes a musician to decide what the musical mode should be for a chapter of the Bible. Her section on modes begins on page 216 of her English book.

A mode is a sequence of notes for a scale -- some may be sharpened or flattened. The mode for the psalm hidden in Isaiah 12 is chromatic dorian. It is the default mode that Haïk-Vantoura uses for most of the prose books. She suggests the hypodorian for Esther, (the book is available here). She also has what she calls a 'strange' mode. La Bénédiction sacerdotale consacrée ne peut être convenablement exprimée que dans ce mode étrange, merveilleusement approprié. She applies this mode to the priestly benediction. I don't see that it differs from the Lydian below with minor sixth - a mode she uses in the psalms only.  All she needs to do is add the darga - low c to the psalm tone.

While I tend to agree that these choices work musically for the purposes she applies them to, I think the decisions and her arguments are somewhat subjective.

Numbers 6:24-25

Some of the modes used by Suzanne Haïk-Vantoura for the music of the Hebrew Bible

The prose books are too much to examine for non-subjective indications of suitable modes but I wonder if the psalms might have some clues. 

Eric Werner in his 1959 book (available here) cites authorities who identify 8 modes in use in the psalms. I am intrigued by the focus on a common word, (1 לַמְנַצֵּ֥חַ below), that occurs in the first verse of many psalms.

The first word is very common in the psalms. It is often translated as 'for the leader' or some equivalent phrase. The Greek translation renders it as Εἰς τὸ τέλος, using an alternative sense for the Hebrew word nxk נצח. In perpetuity is how I have rendered it when the temporal sense seems right from the context. 

Psalms 5:1 - uses two of the above words

I had a conversation with ChatGPT about modes in the plainsong psalter. It makes me think at first that I know next to nothing. Here it is at this link. As usual with the LLM I persist with refining my questions and it is really helpful in organizing what I am getting at - even when my prompt blathers on somewhat. So with that nudge, I should do some more data analysis...