This is an excellent question which I decided to investigate.
I found the following articles:
Dales, J. (1985). [Review of Lingua Latina per se illustrata, by H. H. Ørberg]. Latomus, 44(1), 251–252. http://www.jstor.org/stable/41543604
Monat, P. (1993). [Review of Lingua Latina per se illustrata. Pars I. Familia Romana et Pars II. Roma aeterna, by H. H. Ørberg]. Latomus, 52(1), 239–240. http://www.jstor.org/stable/41536583
Martha A. Davis. (1998). [Review of Lingua Latina: Per Se Illustrata, by Hans H. Oerberg]. The Classical World, 91(4), 298–299. https://doi.org/10.2307/4352082
and this review of the Companion to Familia Romana by Jeanne Marie Neumann:
WHITE, C., & Neumann, J. M. (2018). [Review of Lingua Latina. A Companion to Familia Romana]. The Classical Outlook, 93(1), 47–49. https://www.jstor.org/stable/26506539
The reviews are positive and there are no list of errors which the reviewers found egregious. But on the other hand they are not detailed reviews.
I think, Chad, that you need to remember that this is a book to get people started learning Latin, its not a reference grammar.
So in the first lesson one has to bear in mind the audience. It is difficult enough to teach students who had not suspected the existence of a highly inflected language that the ending of every word in a sentence counts and that nothing can be necessarily assumed form the order of words. One has to aim for some clear rules at the outset and then perhaps modify them later.
I note that your quote from Oxford Latin syntax says that “the verb usually agrees with the nearest member”. I take it that this qualification does not rule out Ørberg’s formulation. I think that teaching that est can take a several subjects or just one is a little too complicated in the first lesson. My reading of Gildersleeve is that Livy introduced the formulation of a plural predicate with multiple subjects
and that this “becomes the rule in Tacitus”.(Gildersleeve 285.3) Ørberg elsewhere uses forms found in Livy so perhaps this is his model.
On “Roma in Italia est” I am sure this word order was chosen to aid comprehension, especially for a reader without a teacher. Perhaps wrongly in the early stages I emphasise to students the variability of Latin word order to make a distinction between latin and English where word order dictates grammatical sense. (Of course I also teach that word order is not random but has to reflect some sense of emphasis of the words used). In time students may be able to take on a more nuanced approach but in the early stages one is just trying to get them in the air however ungainly they flap their wings.
but when I read the first few sentences of LLPSI, I get the feeling that it may not be model Latin (and this seems more important to a reading-only course like LLPSI, compared with the other courses which also use grammatical explanation channels for learning, and so may be less dependent on the quality of their “made-up” Latin to be effective)
This is a fair point. But the textbook is not meant to stand on its own. Ørberg wrote “Latine Disco” to accompany the text and now we have the J. M. Neumann “A Companion to Familia Romana” reviewed above. So the grammar and everything else is not expected to be derived inductively from the text. There are of course a whole set of exercises too which give practice in the grammar. I find that I spend almost as much time discussing these with my students as I do discussing the text.
Ørberg’s text is deliberately repetitive so that students can gain confidence in their reading. Although this is hardly “model” Latin it is highly effective.