I have a possibly similar issue on my H306. I'm not sure about the 3" hole you mentioned, but If I'm otherwise understanding correctly, you're finding water accumulating under the floorboard access panel immediately foreword to the companionway? I've noticed this occasionally as well but not consistently.
I always just assumed it was drip water from the stuffing box since it anecdotally seems to be more noticeable after a bit of motoring. There are limber holes to port and starboard just aft of the motor which allows the stuffing box water to drain to the area under the companionway floorboard and then into the bilge. You might try temporarily plugging those limber holes and seeing if the accumulated water volume is similar to what you would expect to find under the companionway/bilge.
Another possible explanation is the transom hull/deck joint which other H306/290 owners have had to clean out and rebed with something like 3m 5200 sealant. Under power, the lower transom joint gets pulled under the water and submerged and any gap in the sealant will eventually result in leakage. If you remove the panel in the aft berth you'll be able to inspect the inside interior transom portion of the joint which will be stained if there is, or ever was, a leak.
