If you open that hatch again, angle a tape measure in there to measure where the inside edge of each of your stringers start: mark it with a piece of blue tape on your deck.
Not sure what kind of bilge access you have- but try doing the same thing there (might even be able to measure how thick/wide the stringers are if they are like the older stringers. Connect the ltape lines and you,ll know where your stringers are.
5200 and #14's should be strong- use judgement in rough conditions obviously. If you aren't on stringers- maybe con cider toggle bolts or pie plates and thru bolting with a 3/4 starboard or Aluminum backer plate.