I fixed the floor. I can't believe it blended in so well.
I sanded the whole floor with 220 grit and went over it with a tack cloth.
Then I got the palm sander with 150 grit on it and went to town on the shiny spot. I checked every couple of seconds to make sure I wasn't sanding it down too far.
I crossed my fingers, applied the next coat of poly, and walked away. I really thought I'd be able to see it once it started drying. It turned out perfectly.
Unfortunately, everything else I touched today turned into manure. That's okay though. I need a little fertilizer for the perky posies I'll have tomorrow.