Good news! On Tuesday, Peggy started laying eggs again. The sight of her lovely, light-green egg in the nesting box signaled the end of her broodiness. By my math, Peggy was broody for 23 days, which seems fairly standard.
For about half of that time, Peggy was pretty much glued to the nesting box, with only occasional trips to the feeder and waterer. In the second half of her broody period, Peggy stopped sitting on the nest, but still didn't lay any eggs. Throughout, she seemed healthy and relatively happy--except for the times when I removed her from the nesting box. I think I was right to take readers' advice and just let her work out her broodiness on her own.
Now, Peggy's back laying her big, pretty green eggs. It's nice to see them in the nesting box and in our fridge. She's a good chicken, that Peggy, even if she can get a little testy from time to time.