Starting inboard-from the right:

A 1" x 3/8" Ipe band all around the locker lids and the rest of the seat height deck/bridgedeck. That will cover the plywood but I don't think it will even be seen, much. Most important reason for being is to lead water outside of locker lids. You can see it will require a tiny rabbet cut inside along the lids only.

Middle sketch: This is on the side of the lids. Again, the 3/8"x1" band leads water into the scupper drain. Without it-water tension can cling to the bottom and weep around the scrupper channels(it does that now on my boat). This shows the channel detail. This should not only channel water but supports the lid-all around. Perfect flush height with the rest of the deck. No soft spots when you walk on the tops, which you do!

Left hand sketch: Hinge side. This is tricky... I want the best of both-support from the channel and positive drain(no weeping into locker). Putting my compass point on the hinge pin in the drawing, I drew the arc you see. There is enough hinge lift to allow both-support and positive draining-with some shaping of the drain channel edge and the lid band. Hope you can see what I mean.

At severe heel, these will leak but that's not much of a concern-rain is. The actual scupper channel size may be larger for strength and deeper for better drain on heel. I don't want to take any more area out of the opening but my priority is dry lockers.