Slate being hard to breed out? Yes and no.. slate is due to white body skin plus pigment in a layer of skin on the legs giving a visual slate color.
White skin is dominant.. it is 100% dominant so you cannot visually tell which ones carry the recessive yellow skin. That is the hard part, figuring out which ones are pure white skin or not.
The easy part- once you have yellow or green legs, that means white skin is gone(like non-NN out of NN parents). So once you have yellow/green legs you don't have to worry about white skin anymore.
For yellow legs you absolutely have to have the Id gene. It represses the layer of pigments in the legs. Id is a sex linked dominant so if there are only slate or green legs, it has to be crossed in by a new bird.
Your mottled hen has yellow skin but lacks Id. Her mottled legs is due to the mottle also "mottling up" the legs. Her legs not being a clean yellow means she does not have the Id gene.. All of her chicks will be yellow skin carriers- the one cockerel and three pullets from her are yellow skin carriers.
to check for skin color, check soles, also under arm pit etc but laying hens can lose the yellow tint on skin fast because it is the same pigment used in yolk... however their soles should be yellow.
White soles means white skin.
Your yellow leg cockerels out of the cinnamon roo have yellow skin plus Id so those are valuable if you want yellow legs and most of your birds are slate legged. However because their father had slate legs, it means they are not pure for Id.
Those yellow leg cockerels bred to a slate leg hen will give white legs, slate legs, maybe yellow and green legs if the hen carries yellow skin. (if the hen threw yellow or green legs before, she is a carrier and will throw all four leg colors/ If she is pure for white skin, she will throw only white or slate legs)
Yellow leg cockerel bred to partridge hen- half yellow half green legs.
There is no barrier to breeding a yellow legged pea comb bird. The only tricky part is the more genes you want in a single bird, the harder it is. For this reason, any pea combed green leg are more desirable than a pea comb white/slate leg to keep for breeding.
Especially valuable are yellow leg pea comb rooster, he will make your whole flock turn yellow legged very fast.
summary of above:
White skin is completely dominant over yellow skin. It is not sex linked.
Id is sex linked dominant. Id clears the legs of a pigment in a specific layer of skin on legs only.
Slate legs is white skin plus no Id.
Green legs is yellow skin plus no Id.
White legs is white skin plus Id
Yellow legs is yellow skin plus Id.
If the goal is yellow legs and do not want white or slate legs, give big preference to all chicks showing green or yellow legs.
However, Id being dominant, keep some white legs for this reason if there are no yellow leg chicks. Especially if they are known to be yellow skin carriers due to one parent being yellow skinned.
For sex linked mating..
Green/slate roo bred with yellow/white leg hen will give you yellow/white leg cockerels and green/slate leg pullets.
Yellow/white leg roo bred with green/slate leg hens will give yellow/white legs in both sexes.