I also have lice in my flock, though not as bad as you, and I’m also pretty sure the Leghorns and cross Marans brought it.
We don't have permethrin here so i’ve been alternating a pyrethrum+ geraniol powder, a dimethicone spray that mechanically suffocate them, and neem oil.
It works pretty well but whenever i’ve lacked consistency (I only have 18, but that's still a lot of chickens to treat) I find them back. I think you need to treat more than once a week, at least every five days.
Be careful to check for eggs above the vent. And don't make my mistake, when looking for lice you need to check not just above the neck, but also under it, under the wings, around the vent and ears. My infected chickens have maybe only two dozens and they are very hard to spot, especially on black feathers.