She should play First Lady...
Eleanor Roosevelt!
Both are/were 6 ft tall
Both are/were known for their large, toothy smiles
Both are/were strong feminists
And Eleanor hasn't had a movie about her post-White House career at the United Nations since 1982's Eleanor: First Lady of the World starring the late Jean Stapleton.
Geena has even expressed interest in playing her, noting the strong resemblance.
She would just need to practice Eleanor's signature high pitched aristocratic New York accent.