Well, in my timeline I have the Kabars not rebelling because they are given land around Sambat (Kiev) to placate their rebellion. However, as the POD in my timeline is earlier than what I have written here, then it would be different.
Well, there is going to be conflict with the Pechenegs, obviously. Since the Kabars joined with the seven Magyar tribes, when the Magyars fight for the Khazars against the Pechenegs, the Kabars are going to fight too. So the rebellion could be minimized by losses in the war against the Pechenegs.
Another interesting idea I thought of: what if the Kabars migrate to Pannonia, without the Magyars (and maybe with more Khazars too)? Jewish khanate in Pannonia anyone?
As for the nomadic invasions, I had the idea that the Khazar khagan could use the Pechenegs as border guards (kind of like what the Rus' did with the Karakalpaks, A.K.A. Chernye Klobuki) for the Khazars. They could settle on the Khazar eastern border, between the Aral and Caspian (probably still called Khazar Sea ITTL). The Pechenegs would be a buffer for any incoming invasions, which could buy the Khazars a few more centuries of existence.