@Kung Fu Chicken no, a rooster would no help... they are not like, a Roc, or something, they are in the end just a chicken. A rooster will be killed just as easily as a hen.
Sure, roosters give alarms to help the hens find shelter, and will also sometimes bravely try to intervene between a predator and a hen. But in the end, a rooster is a chicken, not a secret ninja warrior with death-defying powers.
It sounds to me like a mink or weasel as well. Hate to be alarmist, but said mink or weasel my be *living in the coop*.
The tracks outside might very well be a house cat. But, "correlation does not equal causation", as they say. Seeing house cat tracks does not necessarily mean the culprit is a house cat. (Although of course it *could* be - it just does not sound like the MO of a house cat.)
Other BYCers have had a weasel living under or in the coop. Is this possible for your coop? For one of mine, it's up in the air about 2' and nothing can live under it without me knowing. The other has a cement floor. Nothing can dig under or through that 4" of cement. Do you have a space under the coop where something could be living? Maybe there is some tiny space you have not noticed, more on the floor level?
So very sorry about your losses... I really hope you can find a solution soon!