Replacing the core from the inside.

I completely agree that plywood is potentially faster and stronger and flatter, if heavier.
You don't always have teak on the deck, but screws and washers would still work. The non-skid probably needs to be renewed anyway. A 6" x 6" screw pattern would be about right for 1/2" plywood, 8" x 8" for 3/4".
Prop it first and use pieces narrow enough to work with slightly compound curvatures. Much easier and neater. Easier to hold the shape by propping too, and you'd reduce potential lumpiness in flat areas.

 

Plywood can be tortured easily if it's thin enough by propping the middle. Unlike cold-molding, which requires pinning down the edges, doing it inside the boat only requires a stick of the right length every so often along the length of a wide plywood "plank".