I'M ALMOST RELUCTANT to give you this right now because I really want to encourage you to work on recto tono chanting on one note for a while, you really can learn a lot from it and it is extremely useful for deeper study of texts. Before going on to some ideas for chanting on more than one note I'll get some old stuff out of the way.
This is the project I said I was working on last month. Well, me and a colleague who is also interested in encouraging a New Chant practice in which People compose new chants in their own language - I say in Esperanto as well,* potentially the "The New Latin for the Church and for Ecumenism" as well, he's not an Esperantist. That wouldn't be as a replacement for singing Gregorian or other ancient chant but to continue with chanting as a developing and living practice instead of antiquarianism.
And about the antiquarian stuff.
In his highly eccentric but interesting and at times useful "Music Primer" the American composer Lou Harrison said:
Old Jewish chants** & also in both kinds of Catholic Christianity (in only slightly modified form). [Note there are more than two kinds of even Western Catholic chant.] They are sung in Temples & Synagogues too, of course. The Psalmtone form is lovely, & one may compose new ones at pleasure. Its full form includes an "Intonation" (beginning tones), a "Tenor" (the "chanting-many-syllables: tone) a "Flex" (a small cadence formula used only to accommodate sentences with several subordinate clauses) "Tenor" again; the "Mediant" (a half cadence formula for the middle of a sentence) "Tenor" again, & lastly a "Termination" (a melodic, slightly ornamental ending motive). An "Interrogation" ending should be provided for questioning sentences. Willi Apel's book "Gregorian Chant" is good on this subject - as are authors Idelsohn & Fox-Strangways on similar subjects. [Look for Idelsohn and Fox-Strangways at Archive.org.]
You are probably confused by that, I've studied chant and it is both confusing and, in at least one aspect wrong, I think, AND, IN ANY CASE, YOU ARE THE ONE WHO GETS TO DECIDE WHAT YOU DO IN YOUR OWN CHANT PRACTICE. You can follow the several outlines of medieval practice - the ones in the Solemnes editions of the Catholic liturgy are more informative and clearer - or any other practice someone else has come up with or you can do what you want to do.
More useful than the above, Lou Harrison finished his Primer with this
Whether rhythmic or not - & there are two basic forms - the Chant is perdurable, a basis to underlie the serious coming together of music & words, & though it is among the oldest kinds of music, still stimulates to hear &to make.
Speaking of "rhythmic" I should note that an alternative to chanting can be found in various traditions of folk spirituals though their purpose is somewhat different. Walter Brueggeman suggested that Psalm settings in the style of blues or country song might helpfully express, especially, the Psalms of protest and complaint and lamentation. I think for more on that James Cone's "Spirituals And The Blues" is especially rich. I'll only deal with chanting here but as this continues I think you'll find information that would be useful for those who want to go on with more of a folk spiritual practice. I intend for there to be lots of ear training involved and am already well into working on that.
I am a bit unhappy to hear someone has made a movie purportedly about the Shaker prophet Ann Lee in which a number of Shaker Spirituals are used in the music. Other than the unaccompanied singing of them, preferably by Shakers themselves, I have never heard any use of them I didn't dislike, not even as set by Aaron Copland. I haven't seen the movie and don't intend to but I doubt they're likely to do any better by that subject than the movies do about any others. I recall hearing the late Sr. Mildred Barker, who was one of the living repositories of Shaker spirituals and, I believe, the last survivor of the Alfred community which had its own singing tradition, talking about how she would repeat a song over and over again to meditate on it, to "labor" on it. I think that's probably a good approach to folk spirituals as prayer.
* The translation of the "Old Testament" by Dr. Zamenhof, the inventor of Esperanto is very good and very singable, it is not a Scripture Scholar's translation from the Hebrew but of someone who could read Hebrew and someone than whom there is no such thing as a more authoritative expert on the language that he invented. Zamenhof's translation is, I think, something of a literary classic in the same way that Jerome's Vulgate, the King James Version, even more so the Tyndale and even earlier Wycliffe translations that the KJV kind of cribbed and the Luther translation is for German culture. Zamenhof's many translations of secular literature are very good, especially Hans Christian Anderson's tales.
I don't hold the New Testament translation into Esperanto done by a number of Christian scholars in as high regard, it's certainly grammatically correct and probably as accurate as any of the other such scholar committee translations are but I find it cumbersome. I don't have the translations of the Gospels by Gerrit Berveling to compare, I've only read his translation of the so-called Thomas Gospel. A good, modern not to mention singable translation of the New Testament into Esperanto probably lies in the future.
** I would suggest, if you want to look into old Jewish chanting of Scripture you in addition to the approved academic points of view, check in to the very controversial work of Suzanne Haïk-Vantoura who claimed to have decoded the musical indications in ancient Hebrew manuscripts of the Scriptures. While most if not all academic experts in the topic rejected her claims, the recordings I've heard of performances informed by her theories are rather stunningly musically coherent, often unexpected and moving and anything but expected. You can hear a number of those on Youtube, though I have to say the ones in which she composed accompaniments for them kind of obscure the musical chanting. Whatever you make of her claims of authenticity, it's worth hearing them put into actual music. Its worth as music is clear to me, at least.