Ok, yeah the problem is the tote is too small. But you are building them a pen already, so that's great! In the meantime, you'll just need to clean out their tote more often to keep them from getting too wet and gross. Not fun, but necessary.
Is the bigger waterer you have now the same type as in the pic? Those are incredibly messy with ducks because they splash alot of water out of them from the sides of their mouths while they're drinking. Can you find an old plastic food container of some kind with a lid to make a new waterer? Just cut a hole in the top of the lid big enough for their heads to get in. That will help alot with the water mess, trust me. 

 Also, it's very important that ducks can clear out their nares and clean their eyes at all times. The type of waterer you had there does not allow them to do this. They can get food stuck in their nares and eyes can get dirty and lead to infections.
Anyway, so I think you have the best bedding (wood shavings), you just need to fix the water situation and size of their pen. ^-^