With my eleven runners, I have been cleaning the brooder three to five times a day. They simply splash a bit of water (I have a splash catcher that does a great job, but I haven't come across anything that keeps the brooder 100% dry), and pass quite a bit of food, not to mention splashing the food some, too.
It is a very short time that they are ducklings - 8 weeks, give or take - this is part of the package. They are adorable, funny, sweet, whacky, and I am glad to have them. Lord willing, they will be eating slugs, bugs, continuing to make fertilizer, and lay eggs, all outside, before too long (it is still very cold at night here).
Cleaning the brooder takes me, tops, 15 minutes, including rinsing out and refilling their three gallon waterer.
Sneezing is an early warning sign - they need to be able to dunk their entire little heads into clean water regularly, to help clear feathers and dust out of their nostrils. Otherwise, they risk sinus or respiratory infections.