I are so smart!
It turns out that I had two problems that were causing water to get all over my basement floor.
The first problem I already wrote about. That seems to have been taken care of by a simple filter cleaning.
The second problem was much more sneaky. And when I say that it was sneaky what I really mean is that I'm retarded.
Even though I had no more water around my air handler, the water in the restroom seemed, if anything, to be getting worse.
In the closet off the restroom is where my water heater and water softener are located. It's also where the drain is for the entire basement. It's one of those little holey things in the floor that I guess ties in with some pipe that goes to the septic tank or something. I'd take a picture but it's kind of gross.
Well to make an incredibly boring story mercifully short I have drain lines from my air handler and from my water softener that I keep crammed into these holes.
The lines from the water softener had somehow been pulled loose, and were just laying on the floor.
So I've reinserted these lines into their holes and now hopefully my wetness problem is cured.