The fossil record is very orderly, and the fossil assemblage we find in one layer is typically only found in that one layer, never above it, and never blow it. I'll show you some abstract examples in which letters correspond to fossil genera that are found in each unit. Blue letters mean it's a marine environment.
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T, U, V
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S
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M, N, O, P, Q, R
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K, L
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I, J
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no fossils
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no fossils
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D, E, F, G, H
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A, B, C
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no fossils
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That's loosely based on the stratigraphy in Dinosaur National Monument, where I've interned and I know the rocks fairly well. You never see any letter outside of the only layer in which it's found. Even though organisms D and M lived in very similar environments they don't coexist. Heck, the layer with D has lots of large amphibians but only 1 type of (small) dinosaur. The layer with M has no large amphibians but tons (literally) of huge dinosaurs.
It seems to me under your model the fossils should be distributed more like this:
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A, K, J, M
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A, B, C, G, H
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D, E, G, M, N, P, Q
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Where fossils don't only appear in one unit, but rather can be found in any given unit and be associated with any other fossil genus who lives in a similar environment. But we don't, and I don't see how one can explain this without faunal turn-over?