After the fall of the Roman Empire, the Latinized population of Pannonia was pretty heavily reduced, limited to some few thousand living in fortified settlements around Lake Balaton.
The whole of northern Illyricum was already underpopulated, and mostly a military frontier, to begin with (there's a reason why Carolingians sometimes called the region a "desolation"). Now, places as Sirmium certainly kept being a, fairly reduced (Sirmium never was that populated), Roman place a bit like Britto-Romans cities in the Vth/VIth centuries, until being weared down by the waves of raids and takeovers of Late Antiquity.
It's really going hard to butterfly this : Illyricum was the strategical soft underbelly of Romania and while heavily militarized, almost every big Barbarian incursion passed trough it. It did a number on a region that wasn't that crowded (maybe 2 millions for the whole of Northern Illyricum), and whom main interest for Romans was less economical than strategical.
So, while I agree it was pretty heavily reduced, it's important to remember that it was such, relatively to Romania as a whole, to begin with. A comparison with post-Roman Britain may be fitting, with a large collapse of shall we say the state apparatus.
While a lot of these remaining Romanized Pannonians were assimilated by subsequent waves of invaders, it would seem that a few of these settlements survived and thrived under the (Pseudo-)Avars, at least for a couple of hundred years.
Kesthely Culture seems a complex happenance : it's interesting as a rural fortified ensemble, but they might not be the only Romanized population in former Pannonia : some fortified places as Pecs, Savgar or Buda, for exemple, can be traced likewise with remains of Roman practices.
Once the Avars vanished from history, though, so did the Romance Pannonians and their language
I'm really wary about the existence of a separated Romance language in Pannonia in the VIth century : at this point, no Romance speech did underwent this distinction already, which wouldn't happen before the end of the VIIIth century, and began around the VIth. Eventually, there's little to no evidence that it existed, and it seems more a speculation (as Britto-Romance) than anything prooved.
apparently the Avars kept them around as an artisan class, and without the Avars they lost their patrons and ultimately were assimilated.
I'm a bit wary about this as well : Carolingian takeover of Pannonia was fairly limited both politically and chronologically, and Slavic principalties soon took the lead of a fairly empty region, and they certainly felt the need to have specialized workmanship (especially as slavic entities were probably part of the Avar ensemble, they might not have been this of a radical change on this regard.)
I'd personally put the shift rather on the relations of Romanized Pannonian populations with the wider world : until the VIIth century, the Eastern Roman Empire certainly represented a huge pole, economically and culturally (as it was for more of the West). If you allow me, I'd use this article : Conflict and Coexistence by Tivadar Vida
On this regard, it's interesting that Romanized Pannonian burials and grave objects mirror what existed in Balkans and Italy during the Vth and VIth century, and overall "strong connections" with the empire.
The decline of Constantinople at this point not only had the consequences of shifting trade roads and making Balkans an Avar playground, but to possibly isolate Romanized populations further.
Being cut from the center of late Imperial civilization, and for the time being from the center of post-Imperial civilization in Western Europe (namely Francia), it's not hard to imagine that the VIIth and VIIIth centuries saw some decline of the post-imperial Roman culture in Pannonia.
The Avar influence on grave can be traced up to the VIIth century, in the same time Roman influence definitely went down in Europe (not just in Pannonia, but as well in Francia, Spain, etc.), and you end up with a growingly mix of Roman ("German" and "Roman" to be precise) and Avar features in archeological finds, up to having by the end of VIIth century, "most" distinctions between what was Avar and Roman, safe some practices and localities, disappeared. It does fit what is supposed about a "revival" of the Avar khaganate (importantly on slavicized lines).
I agree that the Carolingian influence might have been the last blow, figuratively speaking, by becoming the new cultural and economical pole, but I don't think it played this much a major role.
With a POD no earlier than AD 500, what would it take for Pannonian Romance language and culture, or a descendant thereof, to become the dominant culture in the region? Can we get to a point where we have Latinized speakers of Pannonian Romance as the ruling class?
Having Romance Pannonians to blossom to the point forming a distinct ensemble would be already hard : anything about them being the dominant culture would be nothing short of impossible without some early PoD I think.
In the first case, it's the usual answer to any chance in the late VIth and VIIth centuries : advert Eastern Roman decline with shorters wars with Sassanians, and butterfly away Islam. Both of them really took their share on it, and more specifically, the decline of Byzantine influence in the west can be traced earlier than Arabo-Islamic invasions due to Persian wars.
Maintaining sort of continuum (at least economical) between Pannonia and Constantinople would be decisive.
Of course, preventing long, costly wars with Persia is naive : it would happen sooner or later at least until some big political-cultural change in one of the two empires. But if you manage to tweak enough the situation to prevent the loss of whatever remained of Roman Pannonia around Sirmium, at least for a longer time, it would help.
The obviously better situation (but hard to obtain with a VIth century PoD) would be to butterfly away Avar hegemony north of Danube, maybe with a different imperial policy (and maybe not destabilizing central mediterranean situation for the lulz of it, altough it's more a matter about Lombards, and focusing ressources on the Danube). Managing to keep romanized Barbarians in Danube, as Lombards were, would significantly help to maintain the mix of Germana and Roman practices that cans till be seen until the VIIIth century in Pannonia.
Of course, it's hard to tell if it would be a romance-speaking population : personally, I don't think so, at least in the longer term, as Pannonia was really underpopulated. The situation could look more like the Rhine region until the Xth century, as in a mix of germanic-speaking populations in the countryside slowly taking on the cities (mostly as centers of power and trade) and romance-speaking populations in urban or semi-urban settings more or less submersed and assimilated (while assimilating germans on several aspects).
So, not something as Germanized as Anglo-Saxon England, but nothing as romanized as Merovingian Gaul.
To have a Romance ensemble in Pannonia, you'd probably need an earlier pod, in the Vth century at latest.
I could see, for various reasons, a Barbarian foedus (possibly evolving as a Romano-Barbarian kingdom) being firmly established in Pannonia, but with an important caveat.
It would be somehow a "bastard" result, with a distinct Barbarian identity (while romanized) at the margin of post-imperial classical Romania (closeness of Italy, mostly), that would either grow more romanized with time but trough political absorbtion of neighbouring powers would it be a surviving Roman Empire, or a Romano-Barbarian kingdom, either a Barbarian identity perpetuating itself (less as in Anglo-Saxon England, tough, than what happened with Alemani).
