This made me think of the time I've spent with my hand under a broody wiggling my fingers.

Not really relevant given the age of the chicks you're dealing with but I've found it's important to get introduced and hatched chicks at the back of the hen. Lots of hens I've seen will peck at a chick that's in front of their beak. The more sensible chicks make a B line for the hens rear end, but I've had a few get stuck in front of mum, often because they can't clamber over the straw. The mothers just kept pecking them until the chick either got out of range, or got far enough behind that the hen couldn't reach them. Once underneath almost instant calm.
It seems the finger wiggling is much like the sensation the hen gets when the chicks are moving around underneath her. They move around a surprising amount and one could easily think there was no activity from casual observation.
I was very curious about a hen called Mini Minx when she sat and hatched.
She was very cautious about even showing me she had chicks. I used to sit and watch after replenish the feed bowl at a distance at first. Once I was out of reach, Mini Minx would call the chicks out to eat. If I moved back in close, she would send then back under her.

You took your life in your hands if you tried to handle any of her chicks. She was still like that on her final fourth hatch.