I've had only one and she's a hatchery hen, a lavender. She didn't begin until very late, around 45 weeks old, if I recall. Then, she went broody and raised a batch of chicks. Hasn't been broody since and she is over 4 years old now. We call her the Diva Princess, though her name is Shadow. She's a hoot! She is the only Cochin I have, though I now own two of her daughters by one of my porcelain D'Anver roosters. Up until a year ago, she was the only bantam, too.
Since I don't have a Cochin rooster, I can't really say if there are any breeding issues due to their fluff. There shouldn't be, I wouldn't think. Are yours from a hatchery or a breeder?
Oh, and welcome to BYC, neighbor to the west of me!