You could have each story be a new generation with meaningful connections to the prior generation without just repeating exactly what they did. Perhaps most importantly, with the current protagonists shown to be deliberately cultivating their successors.
"There are little-to-no models for sustained and growing multi-generation families including fictional models."
I know you said you don't know of any, but what would you like to see here? Idealistically? I'd love to put thought into this too.
You could have each story be a new generation with meaningful connections to the prior generation without just repeating exactly what they did. Perhaps most importantly, with the current protagonists shown to be deliberately cultivating their successors.
I'm going to write a story and try this.