I know this doesn't answer your question, but...are you already a permanent resident of the U.S.?
If you're not...it looks like you qualify for it on the spot!
The following is from one of the CBSA enforcement manuals:
Under the U.S. Immigration and Nationality Act, Canadian Indians who can demonstrate that they
have “50% or more Indian blood,” by presentation of their band registration card, are entitled to
permanent resident status in the United States. As a result, Canadian Indians who arrive at U.S.
ports of entry and state that they intend to work in the United States are instructed by United States Customs and Border Protection officials to apply for permanent resident status on the spot.
The applicants are immediately issued temporary residency cards and are entitled to work in the
United States without work permits.
Under Canadian immigration law, however, North American Indians are only accorded the right to
enter Canada if they are registered on the Canadian Band Lists. An American Indian can only
obtain registered band status if they can establish that their mother or father was a member of a
Canadian band. Therefore, American Indians coming to Canada to work or study require work or
study permits. Virtually all members of the Indian nations whose traditional lands straddle the border are entitled to be registered under the Indian Act, and once they have exercised this option, they may enter
Canada by right under A19(1).
Some American Indians have difficulty accepting that Canadian law requires them to be registered formally as members of a Canadian Indian band before they can legally work in Canada. BSOs should deal tactfully with cases of this nature.