Canute? I don't think that's a legit pronunciation anywhere....I think Knute should be "nut" or "noot"
I know of one instance where Ace is a nickname for Asa. Had Jessica used in this same fashion, and I may have swooned.
Asa Johnson, Asa Knute, Asa Knute Johnson ---It's quite handsome and not choppy. I like it.