There are at least two wrong points on that post. First of all, Vulgar Latin is very much not Latin; as a matter of fact, it was almost nonexistent up to the fall of the centralized power in Rome, with dialects being very tame things bound to social station more than to area. Indigenous substrata had a ridiculously small effect on Latin; even cases that had been accepted as being substrata (like the Tuscan gorgia from Etruscan) have been disproved.
Thus, vulgar Latin (and in particular the Italic variation) was very much detached from Latin; and that derived from the very collapse of centralized Roman institution (local institutions survived for a surprisingly long time), such as we can't talk about Roman culture after the 6th-7th centuries. Hell, you quoted Strasbourg, but those writings are generally accepted as being proto-French and proto-German, and not really vulgar latin. Italic would work, indeed, and better than the current situation. But how should Italic move to Italian? This leads to the second wrong point, because well...
...no, Italian shouldn't come from a melting pot with Lombard. As a matter of fact, the Lombard overlords fought - tooth and nails - to keep the indigenous population and the Germanic nobility separated. As it was already said, Rotari's Edict was valid for the Lombards, while the Italians followed the old Roman code. The current setup in CK2 is indeed somewhat ridiculous: the common peasant was not Lombard, at all, and the Lombard kings had tried very hard to keep it that way. Of course, that decision was wavering, by 769 - Rotari's laws had been extended to all the inhabitants of the Kingdom one generation earlier, and some kind of melting pot had begun to creep in.
Why, then, I say that you are wrong? Because then Charlie happened. Before said mixture could happen, the Lombards were kicked out of power. This shows in the Italian language, and hard: out of some words, mostly linked to war (the word for war itself, "guerra", is pretty much self-evident), Italian is clean of Germanic influences and looks a lot like a simplified version of late-Imperial Latin. It's not weird: the Lombards, holding a monopoly on leadership, had held a monopoly on war too. Still, a lot of words even in that field (out of the simpler ones) link back to Latin, rather than Lombard.
So, I'd say. Change the culture in Italy to Italic, and Lombard to Langobard (Central Germanic); after 850, if the country is ruled by Langobards, melting pot to Lombard (Latin); otherwise, change to Italian.