For my broody, I ended up getting a dozen eggs from a friend who has three roosters. I replaced the infertile eggs with the new eggs by putting a towel over her head so she couldn't see, lifting her up, and switching the eggs. I was surprised at how calm she was through the whole procedure...
I have a similar problem. Egg production seemed low, so I assumed there was a hidden nest somewhere, but I couldn't find it. Well, I found it today, along with the broody hen who nearly bit my head off when I put food and water in front of her. Here's the problem: we have no rooster, so...