First off I am so sorry to hear what you are going through. I am no expert, but will offer a few ideas to toss into the mix.
First off, ducks need much less heat than chickens and those small plastic containers obsorb then radiate alot of heat from the heat lamps. I know you said there was room for the ducklings to get away, but.... I would say keep the light a foot away from the far end of the container...not over it.
Also I would consider not doing the sugar water for now. I think , based on what you said, it might be way to strong....there is also the possibility if you dissolved it in water using a teflon coated pan the water could be toxic. Better to eliminate it.
Take tap water and boil it in a non-teflon pan and let it cool to room temp, or better yet just use bottled spring water for now. Take you finger,dip it, and drip it on the ducklings bill if it is not drinking.
On the off chance that the plastic storage bin somehow is releasing a toxin when heated you might consider another container.
Check the ducklings rear end... sounds weird but chicks and ducklings can get clogged up and die from what is called "pasty butt". Without a mother or swimming source to keep em clean , they have to rely on us. This is a long shot....but if they were shipped and confined...maybe. If you see poops clogged up, clean it with a rag and warm water and check a couple of times a day....Good luck and don't give up. Those kids will love raising ducks...sometimes things just happen we can't control.