I believe you’re correct. The first reference to Lake Superior being called Lake Gitche Gumee was by Longfellow and Gordon Lightfoot copied that reference in his tribute. One of my older relatives was an electrician who travelled the Great Lakes to repair other ships doing commerce on the Lakes and he was the first person I remember who ever referred to Superior as Lake Gitche Gumee. The nickname has fallen out of use considerably as I’ve become older and I rarely hear it any more.
I knew a women would eventually come along to help the men straighten out their Longfellow.