Your definition of class also seems to be very different from a traditional Marxist take -- hereditary systems were mostly seen as a symptom and not the problem itself, and were mostly orthogonal to any understanding of class.
I _hope_ there is hope, but I don't have much confidence that it lies in century old tropes of "rise up and throw off your chains."
So what did they accumulate? Few acquired power for life; none acquired significant wealth, or a power base independent from the party-state. Even after the end of the union, it was not the former nomenklatura who became new oligarchs: by and large it was the security services and their affiliates who were able to feed on the corpse.
You're right to critique how I described class in the previous message, but what I was trying to accumulate was essentially the above. It's not perfect, but I think this is very much a situation where it's important to not let the perfect be the enemy of the good. I would far rather live in a society where my leaders were once workers like me, raised in the same way, and all men were subject to the same basic economic guarantees. What we live in today is the rule of oligarchs, and it'd be a big step up to merely suffer the rule of bureaucrats.
A very striking way to illustrate this is to look at the career histories of high government officials even very late into the Soviet Union. The last Minister of Coal, Mikhail Shchadov, was born in a village, worked in a mine, went to mining school for engineering, became head of his mine, and thereafter worked his way up the ranks until he was head of the whole apparatus. This story, not that of inherited wealth or monopolistic oligarchs, dominates the histories of Soviet ministers even very late in the decline of the Union.
Where is the "other set" of oligarchs of which you speak? There is none, which means there is hope for workers who might wish to enact fundamental economic change.