I had a H31 1987, leaked also. I had a piece of starboard cut to fit over the top of the companionway above the sliding hatch top, then had canvas shop make a cover that fit over starboard and down over the hatch boards (which I also replaced with a solid piece of starboard), results no leaks into the cabin.
Years ago on the Hunter Forum, I remember someone had removed the "large fiberglass cover that also covers the lines leading to the cockpit" YES it was "somewhat arduous". Unless you really want to take on the task, my solution stopped the leaking. I believe that the sliding hatch not having a downward fall, so the water would drain out was a design flaw, not really fixable and I was not willing to take it on. I just covered it up to stop the leaking.
On the Hunter Owner's site, look up Chuck Creel, H31 boat name "Piano", he recently purchased my H31, recently talked with him and the starboard and canvas cover is still in use, he be willing to sent you pictures.
Bill