We know frustratingly little about the Avars in this period but the fact that they collapsed so quickly after being defeated by Charlemagne indicates that they probably weren’t doing very well. I think if the Avars take over it’s likely that a Slavic king splits off and makes his own kingdom similar to Samo’s kingdom. By the way the link you gave is broken.
Sorry, the better link is
https://en.wikipedia.org/wiki/Bavaria_Slavica and regarding Avars, they had lots of military power thanks to being able to mobilize almost everyone in their population to fight and horse usage tradition, but themselves they were not very numerous (think small, but very trained military elite) and that' s why they collapsed quickly after Charlemagne defeated them - there was barely anyone left to actually fight for Avars and their Slavic subjects kind of dipped out of the war (who made core of khaganate's infantry and navy - when Avars besieged Constantinople from sea, they used Slavic monoxyles as means of naval transportation, because they didn't have any naval tradition of their own), and unlike what happened after Samo defeated them, there was no steppe population to absorb - in Samo's time Avars absorbed faction of Proto-Bulgarians fleeing Khazars, which made them able to stand up to their foes once again, in Charlemagne's times they didn't have such source.
And yes, either they would slavicize themselves by accepting Slavs as equal part of khaganate's elites and numbers will do the rest (Hungarians were more numerous than Avars, that's why they didn't slavicize) or some Slavic leader would topple the khaganate, but it would not happen overnight (if 700 AD is beginning of your Frank-screw TL, Avars might take over Bavaria by say, between 745 and 750, when they clashed agains duke Odilo
https://en.wikipedia.org/wiki/Odilo,_Duke_of_Bavaria IOTL, and Slavic rebellion might happen in the first half of IXth century).
Another kingdom of interest is Saxony. They were pretty strong since Charlemagne had a lot of difficulty conquering them, so they stand to benefit the most from a Frankscrew. Also means that German paganism is around longer
Saxony wasn't a kingdom, but more of like "tribal proto-republic" since in their tribal structure, the highest authority wasn't prince, but some sort of popular assembly, but yes, they would also stay independent and probably dominate most of northern and western Germany.