My apologies for the tardy response.
Thank you, diplodicus & Carmella, for the explanation about y DNA testing. Even though it sounds like it won't answer the Jewish / non-Jewish query, it may help identify Fred H's white grandfather.
That said, the single name studies are unlikely to shed light in this case. This group of Native / First Nations people were Anglicizing their names between 1880-1900. As a result, missionaries were often the provider of a surname at the time the person (adult or child) was baptized. Given that, Fred H's father's surname may have been picked from thin air. Fred H's DNA results don't overlap with any others of the same surname.
Thank you also, diplodicus, for the comment about being Jewish in the strictest sense. This family isn't invested one way or the other in that matter, except to determine, for interest sake, who Marg's father was. The family the man was thought to have come from is reasonably well documented, so it would fill in a piece of the tree. One brother from the family definitely had a child with a woman of the same tribe as Marg.
This is indeed a conundrum. As mentioned, it may only be resolved as more people do DNA testing.
Thanks again for all the invaluable observations.