There’s a Harvey Birdman: Attorney at Law episode where he takes the Jetson’s case and they joke about how they live in a dated vision of the future. I’d probably do that. Maybe have them interact with the modern world but have them appearing posh and snobby despite actually being behind the times on a lot of things.
Would highly recommend you watch Harvey Birdman if you haven’t already by the way OP. I think you’d like it