I think the low C-index is for, like you mentioned, all that grey.
You have a great eye and know what works, just seems like fate wasn't with the sky that day :), if you ever get a chance again, I'd love to see a cloudless version!
Take care, great job! :)
PS. Try using photoshop's selective color tool and see if you can bring the sky to life some more. Image > Adjustments > Selective Color