You are right. It would be a single thin layer of poorly sorted sediments that varied. Not a single layer of silt. And there would be no sorting to the fossils either. We would see bunnies and trilobites together.
Why, if not a single layer of silt, why would there be any fossils?
I don't think we would have any fossils, if the sediments would from as slowly as you seem to suggest. Most likely only realistic way to cause fossils is sudden vast event that buries lot of stuff.
Here is image series that show how the flood came. It started when the original single continent was broken (image 4). In below the first continent there was vast amount of water. When it begun to escape, like in big geyser, the water started to flush all kind of sediments from where the water came. And obviously it would have taken first those animals that are closest and easiest to catch, likely the animals that are not as advanced as some. Mammals are more agile than many other animals, which is why they could have escaped longer. Mammals often can also swim, which is why they don't easily get caught into sediments. That is why no intelligent reason to assume one should find all in the same layer.
And as it is said in the Bible, there were many fountains of great deep. That means, the water came from multiple sources. And there was also heavy rain. If earth was not uniform in the beginning, water from different areas, would have caused different sediments, by what the water could caught on its way.