Options to mitigate rain
We have to prevent the Golf with Rain Problem by addressing the Golf Problem Water Path. We put a plastic bag over the sunroof with magnets; if the water is flowing through a faulty sunroof drain and entering the engine area, this should address it. This *seems* to make the problem less frequent, but it doesn't prevent it entirely in a heavy rain.
A full rain cover manufactured for this model
A full "custom" rain cover made with tarps
A carport
An improvised/temporary "carport": A tarp with hooks set up to easily attach to the fence and the car.
Does the angle of the car affect pooling water? Put the front or rear wheels up on blocks when raining?
Charging options
Purchased: DBPOWER Car Battery Jump Starter 2500A 21800mAh 
This amazing device is not much larger than a laptop battery, and it got the job done on an (apparently) entirely dead battery.
Buy a trickle charger designed for car batteries, about $30. Need to research more. This would involve running an extension cord from the laundry room, would need to be done carefully if it's still raining. How long do they take to charge the battery?
Make a trickle charger out of an old power dongle. How to be sure it's safe and effective? Ask David.
Buy jumper cables and have them on hand. Makes it easier to ask somebody for a jump, and of course a good thing to have to help others too.
Service options
Advance Auto Parts will test the battery, alternator, and starter for free. Need to go back when the battery is better charged, or rather, when the issue with the car not shutting off goes away.