Well, it looks like I spoke too soon!
My Dad found my dottyback lying on the carpet this morning, not moving. He thought he was dead, but put him back in the tank anyway. AND, he swam right off!! He breathed heavily for a while, and seems to have some bruising and looks a bit beaten up, but now an hour later, he seems happy enough. He's swimming about just about as normal, and I've just fed him fine.
It looks like we were lucky, and he was only on the carpet for 1-3 minutes.
This is the SCARILY weird thing - this was early in the morning, at around 8am, so I was still in bed. When my Dad called up to me to tell me about it, he woke me from a dream. And, I was dreaming that my pink (dottyback) fish had died because he'd jumped out of the water into a box! I woke up briefly glad that "it was only a dream", only to discover the news...I'm slightly freaked out about it!
Anyway, I now have a glass lid on my tank temporarily, and plan on getting an acrylic one custom made, with holes and perforations in it.
BOTTOM LINE: I almost sacrificed the life of my favourite fish, despite being told about their habits before, just for the aesthetic look of an open-top tank, and slight convenience (and aeration). IT'S NOT WORTH IT! Get some egg crate, or something else suitable, and do it for your piece of mind, if nothing else.