Do you have the old style hood with studs across the windscreen?
If so make sure that the "bolster" is inside the screen when putting it up , if you don't water will indeed pour through over the header rail. If you have the later "EasyUp" hood then there is probably something which is not aligned properly.
Morgans will never be totally leak-proof BUT they can certainly be made a lot better than having streams down the inside of the screen , even in the heaviest of rain.
