Thank you all for your comments today. :)
Today has been the day from hell, though Ollie really, really did enjoy his dryer time. He got so much of it he finally found himself well done and left the dryer for nap time on the bed.
Fortunately, it looks like the flooding was really just a major mop up. It doesn't appear to have done much, if any, damage. Fortunately, we have a nearly indestructible sheet vinyl flooring (it's original to the house from the late 50s), and I've never been so grateful in my life to not have carpet or laminate flooring. Dealing with an insurance company on top of this would have been a nightmare.
The dishwasher is reparable for a modest amount of money, so it looks like our biggest hit will be from the water and gas bills. The dishwasher ran all night and it ran hot water.
So while we're all exhausted, there's no question it could have been much, much worse than it was.