
Figure 1. Skull of Eorhynchochelys sinensis with DGS colors applied to bones. These differ somewhat from the original bone drawing. This is a standard eunotosaur skull, not a pareiasaur or turtle skull. I see tiny premaxillary teeth, btw.
Li, Fraser, Rieppel and Wu 2018
introduce Eorhynchochelys sinensis (Figs. 1,2), which they describe in their headline as ‘a Triassic stem turtle’ and in their abstract as ‘a Triassic turtle.’ Unfortunately, Eorhynchochelys is not related to turtles. Instead it is a spectacular giant eunotosaur (sister to Eunotosaurus).

Figure 2. Eorhynchochelys in situ alongside manus, pes, pectoral and pelvic girdle, plus Eunotosaurus to scale. By convergence Eorhynchochelys resembles Cotylorhychus.
The problem is, once again, taxon exclusion.
Li et al. employed far too few taxa (Fig. 3) and no pertinent turtle ancestor taxa (see Fig. 4).

Figure 3. Cladogram of turtle relationships by Li et al. 2018. Yellow-green areas are lepidosauromorphs in the LRT demonstrating the mix of clades present here due to massive taxon exclusion. The LRT has 40x more taxa.
We know exactly from which taxa turtles arise.
In the large reptile tree (LRT, 1271 taxa, Fig. 4): 1) hard shell turtles arise from the small, horned pareiasaur, Elginia. The basalmost hard shell turtle is Niolamia, not Proganochelys. 2) soft shell turtles arise from the small, horned pareiasaurs, Sclerosaurus and Arganaceras. The basalmost soft shell turtle is Odontochelys. None of these taxa have temporal fenestrae. We looked at turtle origins earlier here. Turtle origins were published online in the form of a manuscript earlier here.

Figure 4. Subset of the LRT focusing on turtle origins and unrelated eunotosaurs.
Unrelated
Pappochelys nests with basal placodonts. Eunotosaurus nests with the caseid clade, close to Acleistorhinus and Australothyris, all taxa with a lateral temporal fenestra. Li et al. suggested that this lateral temporal fenestra indicated that turtles were diapsids. That has been falsified by the LRT which shows that turtles never had temporal fenestra all the way back to Devonian tetrapods.
Eorhynchochelys sinensis (Li et al. 2018; Late Triassic) was considered the earliest known stem turtle with a toothless beak, but here nests as a giant aquatic eunotosaur with tiny premaxillary teeth. In size and overall build it converges with Cotylorhynchus.
References
Li C, Fraser NC, Rieppel O and Wu X-C 2018. A Triassic stem turtle with an edentulous beak. Nature 560:476–479.
Could you do a DGS analysis for Archaeophis proavus? I’m curious to learn of its true affinities.
I can show you the origin of snakes, but I have only a few taxa within snakes to work with. So once were deep within snakes, I’m lost.
I think Archaeophis would be a good taxon to add to the LRT. It’s known from a complete skeleton with preserved soft tissues (see Janensch, 1906: https://books.google.com/books?id=XEMQAAAAIAAJ&pg=PA24&lpg=PA24&dq=archaeophis&source=bl&ots=4i44DdiOUq&sig=7zauYu-EhvUpXntPGQz6UbxdWlU&hl=en&sa=X&ved=2ahUKEwjXjfuZyIPdAhVM2lMKHbAmA744FBDoATAFegQIBRAB#v=onepage&q=archaeophis&f=false) and there are images online to use (https://en.wikipedia.org/wiki/Archaeophis#/media/File:Naturkundemuseum_Berlin_-_Archaeophis_proavus_Massalongo_-_Monte_Bolca.jpg). Some analyses place it with the aquatic palaeophiids but I’m not so certain.
I checked the links. Unfortunately the skull is not shown in high resolution. The Janensch paper only shows general shape and teeth.
Not sure if this will help but I found a different version of Janensch (1906) with better resolution figures than the previous one: https://www.biodiversitylibrary.org/item/50676#page/346/mode/1up
I will need a good skull. The post-crania is not of much use in snakes.