Also an eggcellent option to do.Since you do have the hen separate and sitting on fake eggs, and have had trouble with the incubator, then giving the eggs to the hen might be the better idea. (I had previously thought she was in one of the coops with other hens, where they could jostle her and add eggs to her nest.)
Or you could split the difference, and give half the eggs to the hen while putting half in the incubator. If eggs hatch both places, you could combine the chicks under the broody, or combine them into a brooder without her, depending on how she does with them.
I think the OP needs to post photos of this Cochin have to say I have a fondness for fluffy chooks
And Orpington are lovely fluffy chooks also.
@Crazy_Beautiful where are you getting the eggs from?