CD Clocks, you did understand that I don't recommend putting the floor mats on the seats, right? That was merely intended as a humorous story of something that happened.
The bed mats that I'm talking about are used in hospitals etc. To protect beds from "accidents". They measure around 32" square and can be purchased in medical supply stores or perhaps even by asking your pharmacist.
If you could find a fitted crib mattress cover or fitted child's mattress moisture protector, you may not even need to do modification. Just put it on the seat with the elastic all around, tucked underneath and around the back of the upper portion of the seat, tuck it into the crease and there you have
it. Temporary moisture barrier seat covers. Easily installed, easily removed for drying after reaching home.