Then the idea is to run a belt sander over the top surface very lightly
to leave the saw marks but eliminate splinters

I would use a random orbit sander.

Are we nuts?

probably :-)

Any thoughts/advice would be appreciated.

I would be concerned that the rough-cut stock would not be flat enough. You
could pull twist or bow out of a board by screwing it down, but if the board
is cupped, and you plane the down bottom side, thew rough side is still
going to have a hump or a cove.

Just something to consider.

-Steve


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