It wasn't the blades I was trying to remove, but rather the whole wiper arms... I had to remove them in order to get the plastic cowl off, since they stick up through holes in the cowl. I did eventually manage it, one side with the batter terminal puller, and the other with an angry yank :-)

Although one time I even had a heck of a time removing one of the blades... the clip part may have fallen off, and it was stuck in, and I couldn't figure any way to get it out other than cutting it in the middle and then pulling the pieces out.

But anyway, I got the wiper arms off and the cowl off, and didn't find anything that looked very suspiciously like it might be causing a leak, so I just cleaned the crud out of there, and then replaced everything, and sealed the cowl with silicone up at the top where it had warped a bit and wasn't fitting tight against the windshield. So perhaps that will help, and perhaps not. I also procured a big sponge :)