It's of course primarily a thought experiment. But I did gave you some narratives myself. If you like, you can share your thoughts on what you think is likely to corrupt a property-free society yourself.
As I said, I think that class is primarily a matter of mediation. Dominant classes emerge because they occupy a mediatory role in the process of social reproduction. Where social reproduction is organised communally, without mediation, class does not exist. The necessary precondition of class relations, then, is the existence of some form of socially necessary mediation. In the earliest class societies, this appears to have taken the form of priest-lords, uniquely able to mediate between communities, between sub-communities, and between communities and divinities. (That last part is I think more important than traditional materialist/Marxist accounts have recognised.) Today, it takes the form of capitalists, who are uniquely able to "embody" capital, on which the entire logic of social reproduction is premised.
Now, I wouldn't categorically rule out the possibility of any sort of mediatory structures reappearing in a post-capitalist society. However, I think what would characterise them in contrast to historical mediatory structures is that they would rely to a great extent on contingent and specific necessities rather than structural and general ones, their power hinging on their ability to resolve a specific problem, rather than representing the entire organisational logic of society. This would suggest that their power would be both unstable, because it is premised solely on the lack of a better solution to a problem, and there would be absolutely no guarantee that such a solution would not emerge, and also that their power would not be totalitising, because it would represent only one aspect of the process social reproduction, albeit a crucial one, rather than being the hub on which the entire process turns. (One could even argue that such partial examples class dominations are found historically, as in the persistence of certain communal practices among peasant agriculturalists. (Ironically, if this were true, it would mean that it took capitalist to fulfil the dominance of the manorial aristocracy.

)) If we accept that any state of post-capitalist implies to begin with a heightened and efficient counterpower, then it would require the further development of this counterpower being critically weakened for one of these proto-classes to actually remove itself in this fashion from the communality of social reproduction and establish class relations.
With all this blether about mediation, it may also be worth saying that this is why I think an authentic anarchism is necessarily communist: because only a communist society represents the dissolution of mediatory structures and thus the containment of power which represents anarchism. Now, one could make a case for an individualist structure within these terms- there have actually been a few interesting attempts to sketch out something to this effect- but any such individualist, even one utilising market-like structures of distribution, would not appear anything like market society as we understand, and so could not be properly described as "capitalist".