More wisdom sought on benchtop detail

Greetings, I'm thickening the top of my teacher's table with stuff on hand. I'm putting a layer of 5/8 ply across the framework, then a layer of short-wise 2x12, then the original maple top. This will give good thickness for the holdfasts I want later, and for dogs.
My question: what if I don't glue the 2x pieces together, just screw them to the top as individuals? It seems to me that letting them float would avoid expansion problems, yet would still give the vertical strength I'm looking for. True?
I'm going to make some sawdust tomorrow morning... I can worry about that gnarly grain later.
"Keep your ass behind you."

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