It is necessary to distinguish between Vulgar Latin and Proto-Romance.
... Labelling points on a continuum is arbitrary,
These two statements contradict each other. Certainly we can define them differently, and even arbitrarily make a distinction between the two at some point in time (or in society or in space, etc.), but since neither one is well-defined (e.g., by large amounts of texts), the distinction is relatively insignificant. That was my point above. I don't disagree with your points, but they are, as you say, arbitrary. Languages don't have historical boundaries, that's just our interpretation.
but when the point was reached that what people were speaking was not what from today’s perspective what would be considered Latin, it cannot be considered to be Vulgar Latin.
There is no such point. It doesn't happen one day that a language becomes something else. Latin didn't one day become Italian (or Proto-Romance, or whatever). And more importantly in this case, the timing doesn't entirely match up: Proto-Romance must have been roughly contemporaneous with the Latin or Ancient Rome, because that's how far back the roots go.
Since we do not know what this speech was like we have to reconstruct it and the hypothetical language is called Proto-Romance.
By definition "Proto-" languages are not attested. So in that very technical sense, we can only apply the term to something we don't have documented. But that would mean that we can never discover a proto-language (e.g., a new tablet somewhere) which is sort of an odd implication.
Vulgar Latin was a real language with dialects and a history; Proto-Romance, which is reconstructed by working backwards from attested forms of Romance languages, is a hypothesis outside time and space and was spoken by nobody.
This is a misrepresentation. Proto-languages
as reconstructed probably never existed as such, but there still was some real-world language that corresponds to the hypothesis (and varies in some details). Proto-Romance (in one form or another)
certainly existed, in order for the daughter languages to share so many features. Various reconstructions have been proposed, and they may or may not be accurate-- but that accuracy is based on real history, whether or not we're able to actually ever check them against real data. For Proto-Romance it's actually relatively easy to reconstruct because we have
so much data. But if you look at another situation, like with Proto-Indo-European, there is a lot more controversy (and less data), and that's a situation where we also still know there really was
some language spoken
at some time, at some place, by some people, but we don't know the details, neither sociolinguistic nor linguistic. Thus no one ever spoke our
reconstruction of PIE exactly as reconstructed, but certainly someone spoke a language that was the ancestor to the related Indo-European languages. So the wording here must be very careful not to overstate things, in both directions.
Now, there is one way in which "Proto-Romance" probably does not hold up as a concept. That is because it did not develop at a particular place in time and space, and then "split" into all of the modern languages, in the exact way that reconstruction would suggest. There were some changes already in place for Proto-Romance, according to the reconstructions, that may have not been in place for Vulgar Latin. In that case, true Proto-Romance would have split earlier (e.g., during the time of Roman conquests) and not yet had all of the reconstructed shared features. How then did those shared features arise? Mutual drift. That is, some changes were already "going to happen" or "in progress" (in some sense) when Proto-Romance split, such that when we reconstruct it,
it looks like they happened before the split, because it was consistent across the varieties. Regardless, this just means that our reconstruction is challenged by complex data, not that there was no such language. Reconstructions will never give us a perfect image of how languages sounded, but they do a reasonable job of telling us that there is a common ancestor and some things about it.
However, when it is remembered that Latin was just one Italic language spoken in Italy in antiquity, it is interesting to speculate whether and to what extent the languages of Italy classified as Romance have descended from or been influenced by non-Latin Italic languages.
Maybe. But Latin itself was influenced by its neighbors, and most of the Romance languages developed outside the domain of the Italic languages, and after they were gone. So you might legitimately find some influences in the regional dialects/languages of Italy, but this does not seem to be the right way to explain Portuguese, for example (although other substrates elsewhere did have effects too).
These languages are very poorly attested, but it seems that some of them were closely related to Latin.
There are descriptive grammars available for several of them, so the situation is not that dire.
Obviously as Rome expanded Latin came to dominate the non-Latin Italic languages.
But again, Latin spread beyond that region as well, and before (all of) the non-Latin Italic languages had disappeared. They're really separate things, neighbors, not just a situation of replacement.
It can be imagined though that varieties formed which were some sort of amalgam of Latin and the local language from which present day languages of Italy are descended.
Yes, to some degree, as I mentioned above. However, standardization at the time meant that Latin mostly replaced the other languages there, and then during the development of the Romance languages they were sort of on their own course. Thus I don't think there was a substantial amount of influence, certainly not something like 50-50 mixing. I'm sure there's some research into the influence of the ancient Venetic language on Venetian (Italian dialect). But again overall this influence was not so strong. For example, the Romance languages outside of Italy certainly differ more (and indeed due to substrate influence!) than those within Italy, for the most part.
It is often said that the languages of Italy classed as Romance differ more from each other than standard Italian (a partly created language) does from, say, Spanish.
Source? There may very well be some standard-influenced features shared in standard Romance varieties not found in dialects, but to say the Italian languages/dialects are more distinct than say Italian vs. French seems extreme to me.
This may be due to the languages being clustered round a centre of origin, but the possibility of non-Latin Italic languages being involved cannot be ruled out.
Yes, it makes sense that, setting aside later contact and merging, dialectal variation within a nearby area (Italy) would be higher than variation farther away. Think of concentric rings of distance, then dialects clustering around social situations.
So I don't disagree that there may have been some influence, but your arguments here seem a bit too strong to me. I suppose one argument in your favor could be that the modern attestations of Italian languages/dialects are heavily mixed with standard Italian, obscuring and thus under-representing the regional influences. Yet there are cases where there is clear influence, such as Greek in southern Italy. There would need to be some explanation for why very clearly Greek features are preserved there, while there is less strong evidence for a direct effect of other non-Latin Italic languages. Perhaps the explanation would be that more distinct (e.g. Greek) features could be preserved while less distinct (e.g. non-Latin Italic) features might merge.
Unless archaeologists come up with significant finds we shall never know.
Certainly some details remain mysterious, but have you looked into the better attested cases? We really do know something about many of the non-Latin Italic languages, and I'm certain that someone has looked into this influence. I haven't read that research myself, but I'm sure it's out there.