I feel your pain, i have about a dozen broody birds right now as well hogging up the nesting boxes, my egg production is steady so they are allowing other birds to sneak in and lay, but it's still annoying...
Worst are my three Black Sumatra hens that are broody, they are fierce defenders of their nest and unlike most hens that just complain when you reach in the Sumatras will do their best to draw blood, and I mean that literally... I have to reach into the nesting box with my hand up high and come down on the Sumatra's head and forcefully remove them from the nesting box before attempting to collect eggs, or risk bleeding or eggs with holes pecked in them...
I also have several bantams that double up in the same nesting box to help other chickens sit on eggs...
The only positive side is that because the bantams and Sumatras are broody, I'm not getting their smaller eggs that I have little use for... The Sumatra eggs are about a medium sized egg but they look miniature when you put them in a carton with Larger and Jumbo, plus they are my only white layers so the token 'small' white egg stands out like a sore thumb...
On the small egg front, I apparently have a guinea with some egg making issues... I know 'fart' or 'fairy' eggs happen every so often and I have had them every so often, but lately I have literally been finding a guinea 'fart' egg every single day in one of the nesting box for at least two weeks now... And go figure it's the only guinea that is actually using the nesting boxes, the rest just lay all over the coop...
two of them a couple of my more favorite girls. We also had to put down some birds on Saturday that we got ill. They were quarantined but the flock seems to have some minor respiratory symptoms. We are treating with antibiotics and will be sending out some birds for necropsy. Thankfully we have some spare cockerals. 
