Dumping my thinking

Depending on how discoverable or custom are each page, that could be more or less automated.
But I think as a first step, you would need a logic that knows how to pull common things for a given family version (maybe display recent versions of that family) and the rest of the page fully manual, like it is today for the second half of the page.

BTW are you referring just to the landing page or to the whole documentation subtree (say with faq, getting started etc)?
That's more work but I know Ceylon does it that way. they copy the given tree and update. Not a lot of projects do that though as maintaining that many documentation versions is a significant toll. It also makes the latest and greatest on more equal footing with old versions which might be an undesirable effect.