Upon inspection, it turns out that a bolt holding the rear rack to the bike has broken, and the rack is bouncing against the frame of the bike.
I'm not entirely surprised because the baggage weight on my rack (a very strong rack from Old Man Mountain) is probably carrying much more than its recommended maximum due to today's extra two gallons of water.
Fortunately, I have one extra replacement bolt for this. Removing my rear saddlebags and changing the broken bolt (which didn't want to be removed, at first--I'm glad I brought that set of pliers with me) delays me for 20-30 minutes, just as dusk approaches.
Darn it... It was looking like I just might reach Willow Spring by dark, but now I know I won't.