Questions On Rebedding A Wooden Hatch

[RLewis]

Hi all- I have been searching this forum and have found lots of useful information on rebedding hatches but all of the posts seem to be for aluminum frame hatches with a metal mounting ring to keep the entire assembly together and leak free.
My question is on my 1981 Taiwan boat with teak decks, I have a total wooden hatch. Very heavy and looks real nice. But I have a leak. I used a hose to track the source which is at the forward port corner of the hatch, and have nearly removed the headliner in and around the hatch. My question is on rebedding this wooden hatch. The inside of the frame work of the hatch opening that you see from inside the boat clearly has several plugs that are covering screws on all 4 sides. I am assuming that the hidden screws are penetrating the core of the deck to hold the hatch assembly in place securely and that the sealing caulking material is then placed in the small space between the hatch frame and the cut out of the deck. Now- I have teak decks so there is another "layer" of material that needs to be sealed to the outer side of the hatch frame.
Do you think I will need to drill out the bungs that are covering the mounting screws and pull the hatch completley out of the hole that it is mounted into?
Is it possible dig out enough caulking material from the top side to then reseal the perimiter of the outer hatch and have a resulting decent seal?

I confess I have yet to see the true underside of the deck as the headliner will be out tomorrow and may reveal more details of how the hatch is actually mounted in place.
Any suggestions from those more experienced is greatly appreciated.
Thanks Randy