Hi Chris. It has rained like crazy today and the car was parked under dripping trees. The hood compartment drained out no prob and the area behind the seats stayed dry. So I guess you're right, it simply pours in when the car brakes.
The plastic rivet things come out easily with care. The rear liner lifts out when you unscrew the lid stay. The lower liner then just lifts out. It will be sodden because it is foam backed. There are two rubber bungs. Take them out and the water is conducted out below the car.
I found that the water is coming through the bottom of the window seal. Need a new hood!
I used to have a Wartburg and the windscreen leaked, filled the tray under the dash, then shloshed the water all over my feet! Great joy!