Many, many thanks to all three of you for jump-starting this into a successful search. It turns out that Jayne's memory of the closing lyrics is correct -- but also, on a bit of further listening and poking about, that they're essentially the closing half of a framing theme song. Unfortunately (though not surprisingly), the Wayback Machine video quality is uneven, so there are skips in what I'm hearing, but with the prospect of more episodes to be found, I think I'll have a full set of the framing lyrics before too long, and by the sound of it there is more to be found in the body of the films.
Meanwhile, further credit where due: the screen credits indicate that the music for these was "written and sung by" one Stan Davis. That name isn't immediately familiar to me, but these surely won't have been his only credited songs, so I now have an artist to research as well.