Actually, using soaked, fermented, etc feed is a benefit as it offers not only nutrition, but hydration as well. It also makes the feed more palatable and encourages consumption which is helpful in chicks that need to eat. All my broods get 1-2 feeds of soaked feed from the start and thriveChicks actually should only be on dry...
I ended up rigging a bird feeder at almost face level for the chicks. It didn't completely stop the mess but it was maybe 80 percent better. Keeping those little feet out is a huge help.