WoP:
Left communists don't wish to replace the current state. We seek to dismantle it.
Mass assemblies and workers councils are historical forms that have typically arisen on the shop floor in revolutionary situations, we don't and shouldn't fetishize them. We advocate organic working class political structures because we advocated the working class.
If you're caught up with the lingo, the terminology-- I really prefer to call the state-apparatus during the dictatorship of the proletariat a "semi-state." Either way we're arguing semantics.
The working class, once it realizes the power it has to make change when collectively organized, will form organic structures useful to the actual insurrection of capitalism and in the periods directly after.
I'm not a theoretical guru...but you shouldn't confuse the state, the party, and the vanguard. The state is a conservative force that should be eliminated. The international proletarian party will be the vanguard, and the party should never be merged with the state.