Why not replace the players with bots, who post moves from a list of past greats? Then it would be very entertaining to read, and a lot less trouble to contribute to.
Or we could extend the preview facility - pressing the preview button would e-mail the suggested move to all other players, who would then vote on whether or not to allow it.
... until eventually, there will be just the one player left who will descend into a preview hell of their own making.
Joking apart (who says we're joking? Ed.) how about a small variation called, say, Second Post - where we have to post TWO lines at a time. So you'd either cop the first two lines, the second two, the last and first, the second and third or the fourth and fifth. Might make for more cohesion. Or lunacy.
(Chalky) Lines that rhyme should not be permitted as a combination, as I have pointed to someone out in Another Place. Makes it too easy. But other combinations might work.