The nine Gregorian tones are probably the most direct historical link.

That being said, the use of tones originally intended for communal singing as a solo musical form has no historical precedent whatsoever. The Gregorian tradition is florid melisma for verses sung by cantors vs. the entire schola, whereas the modern "tradition" is to couple a comparatively intricate people's part with a simplistic cantor part. Through-composed responsorial psalms for the cantor are a resource desperately needed in the modern Novus Ordo which seems to be completely out of mind for most publishers.

New compositions? I thought the mandate for the GS was to find simpler chants in the Church's treasury.
Does anyone here know of published history of the divergences between the forms of the chants between the readings as in the GS and as in the lectionary?

The USCCB gives a list of approved psalms
http://www.usccb.org/bible/approved-translations/index.cfm

The Gregorian tones have historically been those used in the Novus Ordo and the Latin Rite. I prefer the Gregorian tones. Whatever you decide to use, I think it very important that the text of the psalm match the missalet or pew Missal that your parish uses. I can't tell you how many times I've encountered the cantor singing psalm text that doesn't match the pew missal, even though they sang from an approved source.

With the caveat that there is no clear official statement of intention, so this is my interpretation

take some imagination to notice any similarity to ancient responsorial (antiphonal) psalmody

There is no similarity to antiphonal psalms, because the intention is quite different. They are supposed to be reponsaries/responds/... One clear mark of this difference is in the alphabetic indices, thus in GS the antiphon Ad te, Domine, levavi in the Introit index is marked as '4', i.e. mode 4 for the psalm (from which the antiphon is drawn); for the Psalmi Responsorii Ad te, Domine, levavi is marked 'C 2 g' (with responsory verse Docebit mites vias suas).
It seems that the reformers, in obedience to VII, were putting psalms into the lectionary not just quotations from psalm verses, which is mostly what the Gradual has. The intended form is shown by GS, a psalmist chants to a simple melody, akin to the other lections, and there is a response (in the form of a verse selected from the psalm) made by the congregation or schola after each verse. Bugnini says this

Songs between the readings [Reform .. p.423]
... the entire system of chants was revised. The responsorial psalm that follows the first reading is chosen in function of that reading and completes it. The verses of the psalm are grouped in stanzas of equal length in order to facilitate its singing by the psalmist or cantor. The refrain, which consists of the most characteristic and meaningful verse of the psalm, explains why this psalm has been chosen.

What was the point....

The GS was created to meet the demands of Sacrosanctum Concilium #117: “The typical edition of the books of Gregorian chant is to be completed; and a more critical edition is to be prepared of those books already published since the restoration by St. Pius X. It is desirable also that an edition be prepared containing simpler melodies, for use in small churches.”

This was written in 1963, in the very first document of Vatican II, and the GS was completed by 1967. In 1963, except in cathedrals, religious communities, and very well-heeled, well-trained parishes, one only rarely heard the Propers sung to their authentic melodies at High Mass. Most often they were hastily sung to a psalm tone or to a tawdry setting in a quick-n-easy Romantic style, by choirs who could hardly handle even that. At Low Mass, they weren’t sung, and the congregation sang some hymns to pass the time.

So in ‘63, the goal broadly was to rejuvenate the sung liturgy worldwide, by getting every parish to chant according to their ability, and a book of simplified chants theoretically might have achieved that.

But when the vernacular liturgy became the norm by the end of the 60s and singing the new responsorial psalms from the lectionary became the unofficial norm, the GS was kind of like the Blackberry is today: pretty innovative and useful and still technically functional, but socially, everyone’s been chasing iPhones and Androids for years, and has forgotten about the BB.

Additionally, it’s always seemed to me that the development of the GS was not coordinated well with the production of the new Missal/Lectionary. It was simple enough to redo the actual Graduale Romanum to fit the new calendar, but the GS doesn’t match with either the ancient chants of the GR, or the Missal/Lectionary antiphons, psalms, and alleluias. Thus we often have three completely different sets of propers for a Sunday, whether one is following the Missal, GR, or GS. One can legally sing either, with equal approval, but it takes a load of explaining to anyone accustomed to seeing only one set of texts in their hymnal/missalette/app.

I don't have a copy of the Lectionary, but I understand it contains what are called the Common Psalms, a selection of psalms and antiphons to be used on any day in the designated season‡. This is a translation of the relevant section of GS. No one takes any notice of it, in my experience no one ever moves beyond the first option that comes to hand/eye
I attach a page from a very early attempt by John Ainslie to provide an English version of GS. It shows several of the reasons why it did not catch on, none of them to do with Ainslie and his collaborators. 1/ three weeks after publication, the Season of Epiphany was abolished! so the book looked instantly out of date. [ the first edition of GS was also outdated by the calendar reform, and the second edition was not until 1975! ] 2/ the psalm is presented in single verses, while the NO lectionary deliberately prints in stanzas. 3/ the rubrics changed for the NO. 4/ and the NO lectionary only uses a single verse at the alleluia, whereas this offers several. - All these are problems with the first edition GS, which Ainlie follows faithfully.
‡ See this.

In some places it was that bad, others better. Individual parishes have different levels of resources available and nothing has changed in that regard. You find the same today as 50 years ago.