I think I've got it

The dad time travels into the past, uses the punch cards to redirect a missile test into outer space, and that causes the meteor to never hit the moon.

How does he time travel?

Turns out all those black holes sucking up people were looking for him. An entire city (Seattle) was cleaned out, trying to get his dad. He's next. Of course, to stop the moon, he has to lose himself in the vortex (because the actor is working on another show now).

So the rest of the family now has to time travel as well, trying to restore the future and preventing apocalypses, as they search for their dad (who may or may not return, depending on production demands).

Alternatively, the time travel kills him, but restores time to its normal state. All those black holes, and demons, and "dragons", and such were all just temporal and spatial rejects due to time manipulation experiments conducted by the radio DJ and others, to stop the asteroid from blowing up the moon. Once the moon is safe, the time distortions never happen, and everything goes back to normal. Except... one of his daughters manages to rescue him before he dies.

Sure it's a paradox, but it's not like the writers care.

And the show ends, with no need (or justification) for a renewal.