To get the tent all squared away, I purchased some Gear Aid (previously McNett) Zip Care Cleaner and Lubricant. It's probably some expensive scam for what it is, but I spread it on the zipper and it was like magic. I'm not sure how often I'll need to reapply it - but with 2 oz. of this stuff, I've got plenty to last quite a while.
Problem solved. ...And honestly, I don't think that the problem would have solved itself as I was originally hoping - once the zipper gets dirty, it's too hard for it to clean itself.
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