I have had to repair the door you are describing as well as the door to the head, the ice box cover/nav table sliding channel.
What I do is take some solid wood. I have use pine but a hard wood may give longer service. The pine will outlast the plywood used by the factory.
Anyway...I take a pocket knife and whittle a sliver of wood, dip it in epoxy -then tap it into the screw hole. Then take another sliver of wood and continue filling the hole this way. after the epoxy has set you can re drill the hole.. I have screwed it together before the epoxy set and it did work but it may not be as good. this is a good time to get all the screw to be the same length and diameter. Use as long a screw as possible but use the original screw diameter so hinge does not bind on the screw head.
