Sounds like some adjustments are needed !
My guess is that you may have set up an unintentional cycle that makes the problem worse.
Ducklings need water available at all times.
Ducklings splash.
I have cut down 80 to 90 percent of the wet bedding problem by doing a couple of things.
Please, please let your ducklings have water all the time.
By letting them go without water, you create a panic. (It really is dangerous to their health.) When they are panicked and dehydrated, they will splash much much more. They will also drink too much, too fast, and throw up water all over the place. So if they have water available, and know it will be there, their splashing is not nearly so intense nor frequent, they won't overdrink, they won't throw water up all over.
So what they need is a splash catcher.
I have used a two-piece broiler pan with a washcloth under the waterer. That works very well. You can also place a shallow plastic bin lid under the broiler pan. I have eleven ducklings. The broiler pan held two quart-size waterers or one gallon-size waterer.
The splash-catcher I am using now is a large steel salad bowl with a ricotta cheese tub upside down. I punched a few holes near the top of the cheese tub so water will flow through it. I place the gallon waterer on top of the cheese tub, in the salad bowl (I think the salad bowl is about a two-gallon capacity, about 8 inch diameter).
This lasts them about 15 hours overnight, about four hours during the day. If I had to be away all day, I would set up two.
An advantage of the salad bowl is that if the gallon waterer empties (it has happened for a short spell, perhaps 15 minutes before I caught it), they can still get water from the bowl for a while. They even pushed the empty waterer over and drank directly from the bowl without making any more mess than usual.
Another thing I have done is separate the bedding so that the bedding that is under the waterer does not contact the bedding closer to where they sleep (so the sleeping bedding doesn't absorb water from the bedding under the waterer).
Again, please let them have water all the time. Their personalities will be better, they won't panic when you finally give them water, and they will be healthier.