How about changing to a set of perspex flaps,more solid, and put on a light elastic cord to them to hold it shut.
The elastic cord to them to be not so heavy as to allow the water to flow out ?
Or use perspex flaps again but weight it on the outside so as to again close them against the sea water but inside water can get out?
A point that struck me was that the flaps are a long way from the water and I wonder if the inside water was needing to be large to reach the flaps and flow out.
If thats the case, maybe the water is not getting to the flaps but choosing a side of the boat to flow to and gathering that side. Slight list then is exaggerated with more water?????