Ahh, 31 or 32 years! Our lazarette hatch has its original finger pulls, similar to yours but by Perko, on both the forward and after edges. Someone added hinges on the after edge so the after pull is no longer useful. Our 46 year old LeComte sailboat has elaborate sliding latches operable only from within the cabin to keep prying hands out of the lazarettes when the boat is locked.
I'd search around for flush, locking hardware (never seen any for an exterior floor...), or perhaps you should patch the Teak and add a LeComte-type of sliding latch operable from your aft cabin. The latches consist of knobs reachable within the cabin, threaded onto sliding square-section rods, square holes in guides for the rods, 'L' shaped bits welded onto the rods that slip in or our of bent plate eyes on the bottom of the lazarette hatches.
A lot of fuss-n-feathers! The sliding windows on Revel do not latch and the aft sliding door lock is rather light duty and operable by old-style skeleton keys.