re: How to uncup live edge wood

That’s an awfully thin board to work with for a top unless it’s perfect.
You can do a plunge slideing dovetail across the grain on the underside.
Install segmented dovetail blocks spaced out underneath and then attach a “stiff back” piece to the dovetailed blocks to flatten out the top.
The plunge method will allow the dovetail groove to be hidden from the edge.
I like to wax the dovetail groove to facilitate expansion and contraction.