The models don't have memory per se, they just process the entirety of the context (i.e. the conversation) with each generation. As this becomes larger and more complex, models with less parameters struggle.
You can try to add certain instructions into the system prompt, such as "advance the story" but ultimately, more parameters means better grasp of the conversation. I haven't come across any model below an 8 bit 13b model that could keep a story together, so that's the minimum I go for when I want to RP.
As for the 70b's writing being less interesting, I'd say that's independent of the model capabilities and more down to style. Again, giving it instructions on how to write as well as example messages can help but it does somewhat come down to what it was trained on.