Actually, turns out the most likely--or at least exciting!--scenario based on my symptoms is that my kidneys are wired wrong. One of the tubes running from kidney to bladder is not attached in the correct manner, and is...doing something else. (I didn't ask whether it's spraying through my abdominal cavity like an unmanned fire hose, or just is hooked to the wrong thing, since I was too intrigued by the notion in the first place.)
Apparently that's not terribly uncommon a congenital condition, particularly in women. They can even fix it. Dramatically.
"Actually, we'd open up your flank, and take out part of your kidney," he said.
"Dude." I said. And then, after a moment's reflection, "Well, hell, I'd be under general, what would I care?" (Although I bet recovery from THAT hurts like a mutha. Kidneys aren't known for their painless and forgiving nature.)
So next week I go in to get shot with dye and X-rayed to check for the wiring issues, and I'll hook up with their lifestyle/biofeedback person to see what's going on.
And nothing got inserted anywhere horrible, so I call it a good day.