I have Pivek (Pivk,
Pink) in my tree too. Several of my grandmother's step-brothers and step-sisters were Pivek. Have you checked
Ellis Island yet? I see your Joseph Pivk died in
Cleveland Ohio. That had a very large Slovenian Community. Mine went to Waukegan and one boy went on to
North Dakota and then to
Racine Wisconsin. There may be some information on the Slovenian Genealogical Society International Web page. You might find something in the
Trunk report. There was an M. Pivk in Altus
Arkansas in 1899. There were two Pivek families in Waukegan (unrelated as far I know).