Wow that is a lot of water, I would take the door panel off at some point and try to clean out the bottom of the door.

 

Had the very same problem with my DS door. Got in one day after heavy rain here in FL and heard water swooshing around. Turned out to be my drain was clogged once I unclogged it water was gushing out like your PS door. I since took off the door panel and cleaned up the inside to avoid rust. And I also unclogged the PS door drain just to be safe.