I think it can all be easily handled with timed drops. Simply state a deadline, like 30 minutes or an hour and enforce it. If peeps miss the deadline by a couple of minutes. Cool. If they miss it by an hour or so, have a mod close the battle and withdraw your verse. There's a difference between missing a deadline cuz your computer froze up. That's missin it by a couple, ten minutes at the most. Cats are clearly pre-writing or suffering writer's block if they miss by too much more than that.
Simple. Have the mods (sorry, more work for you guys) enforce the timed deadlines. That's how to solve the problem.