On our site, the Author Names for a K2 Item link to a list of the Author's items.

We'd like the Authors name to link to their profile.

Or, we'd like to link to our own custom K2 item that would be the authors profile.

Please advise how we might do this.

You could do this on your overrides.
This would be a manual procedure. If the author's name or id matches then link to the X item instead of his user page.