I agree that Elijah Cade sounds the best! But if you are set on Noah I would pair it with something that doesn't end with tha -ah sound, like Elliot Noah or Noah Ellis. Hope this helps!
When I analyze baby names, I like to think of the child's name on a kindergarten roster.
Actually, I'm seeing a lot of Elis pop up...I think it's because Elijah has become so common and not quite as unique as it was ten years ago, when it first started spiking as a trend.