although I think the African Romance of Carthage would be rather separate from the African Romance of Tingis.
I think that's quite speculative to be honest : we don't know anything about Romance speeches in Mauretania, or even if they really emerged to begin with.
Now, without having much to support it, I'd rather think that if Romance speech was to root itself in coastal Mauretania, it'd be closer to Hispano-Romance speeches giving the social-cultural proximity with Betica.
We can guess it was similar to Sardinian, and perhaps also the Latin of Sicily before the Arabs arrived.
While there is a known proximity with Sardinian phonology, and maybe Hispano-Romance phonology, I didn't saw Italo-Romance being mentioned.I was under the impression that the thin knowledge we have about it would make Afro-Romance more of a south/western Romance language, but I might miss something there : what does make you think about a possible connection to Italo-Romance?
But I wonder how far things might go in the direction of local languages.
They were certainly more present, (Both neo-Punic and Berber) in African provincial culture than their counterpart in western Romania (Gaulish influence is not even superficial, and Germanic influence is mostly phonologic and vocabulary based in Gallo-Romance for instance). I'd expect Berber, in the case of a Berbero-Roman ensemble pulling a Merovingian in the VIth, to at least play the role of Germanic speeches in Gallo-Romance, with the distinction having another important language being spoken already in the region (and likely survived as Afro-Romance until the XIth to XIIth centuries). Now I agree that Neo-Punic might disappear earlier ITTL due to being itself importantly Berberized in Late Antiquity, but that would reinforce Berber influence IMO.
But if we took 4th-6th century Vulgar Latin inscriptions, epigraphy, etc. from Gaul, Hispania, etc., would we be able to guess the development of the Romance languages of those regions, as we might from 4th-6th century Vulgar Latin in North Africa?
There's no much vulgar Latin written sources tough : Merovingian Latin (as a form of Late Latin) for instance is more a decomposition of classical Latin rules than representative of the evolution of common speach (for exemple, Merovingian Latin uses variant of classical cases essentially as a decorative tool, while Vulgar Latin does reduce and systematise them).
Most of what we know of Vulgar Latin forms comes from partial epigraphy since the beggining of the millenium, sources written in classical Latin, some features of
Late Latin and reconstruction from early distinguished romance languages (such as in the Oaths of Strasbourg).
What we know of Vulgar Latin at this point doesn't really help highlight the regional differenciations, because all speeches went trough the same development altough with various result depending of ad/sub-strates and contingential events. If you're interested this site provides with a lot of information.
Now, you're right that we can deduce something of African Late Latin trough Spanish sources, for exemple. I don't agree with the author that Africano-Romance had such a marking influence into the making of Ibero-Romance phonology, but African Latin certainly did had an enormous prestige in Spain, as well as an Afro-Romance adstratum. Still, the comparison with Sardinian might be more fructuous at this point.
Eventually, for what matter Afro-Romance, we even have less exemples than usual, due to scaracity of aformentioned sources, a more important connection to late classical Latinity, etc. and the more important survivance of non-Romance speeches in Africa (and their possible substratic or adstratic influence on Africano-Romance) make it a bit distinct there.