HI Lovefish, sorry to hear what is going on.
This is the first I've heard about it.
Since you have the water and filter media, I don't see why you would have to wait 24 hours before putting them in the new tank. I would put them in it.
I would definitely get an airstone working so the water will have oxygen. If you keep the glass over the tub is not good, there isn't enough oxygen getting to the fish.
Once you get the fish in, just understand the tank may undergo a small cycle (even if the filter media is still good). I would test every day to make sure the ammonia and nitrites don't get to high.
Good luck and get those fishies back in their new home.