You mentioned a "massive clutch of eggs". How many eggs is she incubating? This can dramatically affect the hatch rate (% of fertile eggs that hatch).
I often see a 100% hatch rate when the broody hen is incubating 6 to 10 eggs. I recently allowed a broody hen to incubate 14 eggs, and noticed that one of the eggs in the center of the batch pipped and zipped, but was not able to push itself out of the shell because the other eggs were pressing in around it on all sides. I did an assisted hatch because the membrane dried around this chick, making it impossible for it to hatch on its own.
Someone on BYC (sorry I don't remember who) said that they see increased chick mortality at and just after the hatch when broody hens try to hatch out very large clutches. If I recall correctly, this mortality was in the form of chicks being unable to make their way out of the shell or being more vulnerable to crushing due to a large number of eggs and chicks.
The other complication with really large clutches is that the hen can only cover so many eggs successfully. If the clutch is too large, there will be eggs that extend outside the hen's coverage, allowing them to cool down. As she periodically rotates the eggs, eventually all of the eggs are subjected to less-than-ideal incubation temperatures. This can substantially reduce the hatch rate.
For the most successful hatches, it's best to set no more than a dozen eggs under the broody hen (that is, eggs of the size that she typically lays).