--Theropoda including Marasuchus, Herrerasaurus and Trialestes
---- a clade of Pisanosaurus, poposaurs and silesaurids
----- Sauropodomorpha including Saturnalia, Thecodontosaurus and Massospondylus
------ Daemonosaurus + standard Ornithischia
Why is this? I set out to determine the reason. First, I deleted most taxa Peters finds outside Dinosauria, leaving Turfanosuchus and Gracilisuchus as outgroups, as they are close to the base of Avemetatarsalia's sister group in both his and Nesbitt's phylogenies. This way I don't have to deal with all the unrelated taxa I'm unfamiliar with. I also kept in Arizonasaurus, to see if poposaurs would group by it instead. His same topology resulted when I ran this in PAUP, so my deletions didn't affect that. Enforcing traditional Dinosauria and Saurischia took 28 more steps.
I added the 15 saurischian and 11 dinosaurian characters from Nesbitt's analysis missing in Peters' (and also one I thought was coded for- the subnarial foramen, but it turns out Peters only codes for a subnarial fenestra). I used Nesbitt's codings for these, also coding Massospondylus kaalae, Pampadromaeus, Panphagia and Daemonosaurus myself. The new phylogeny excluded Marasuchus from Dinosauria but was otherwise largely the same. It took only 5 more steps to make traditional Dinosauria and Saurischia. A reduction in 23 steps isn't a bad start.
Then I started going through Peters' characters, making them ordered when needed (which sometimes involved rearranging states), and making sure each was only coding for one variable. Luckily, with the non-dinosauriforms mostly deleted, a lot of Peters' characters had far less states in included taxa, so this was much easier than if I were to try it for his whole analysis. Still, it's mighty tedious, so I stopped after doing the 115 cranial and dental characters. During this process of fixing characters, I found 32 miscodings. Being the first taxon in the list, I decided to code Turfanosuchus for these first 115 characters, plus the three extra characters I had spun off of them to keep each one only coding for one variable. Turfanosuchus was miscoded for 33 characters, or 28%, which is pretty terrible. Running the analysis found..... traditional Dinosauria and Saurischia.
--------- Sauropodomorpha including Saturnalia, Thecodontosaurus and Massospondylus
--------------- Theropoda including Herrerasaurus and Trialestes
It doesn't perfectly match the consensus, but I didn't add any characters for e.g. Crurotarsi, Ornithischia including Pisanosaurus, Sauropodomorpha including Panphagia and Pampadromaeus, silesaurs+dinosaurs, so the fact I didn't get these clades is hardly surprising. What was surprising was how soon this happened. Adding 26 characters and changing 65 cranial states, half of the latter in the basalmost outgroup, and the traditional phylogeny shines through. So why does Peters' analysis find odd topologies- it lacks enough characters, has poorly formed characters, and has numerous miscodings. Fix even a fraction of those issues, and it resembles the traditional consensus.
Below are the gritty details of my alterations, for those who want to slog through them.