My first choice would be to use the very word you did: "indigenous". My second choice would be "aboriginal".
I'm a Canadian of European extraction and my understanding of usage is mostly gleaned from casual media consumption and discussions with an older relative who had a senior management role in education in northern Manitoba, where most of the population is Cree. When he was active 10 years ago the preferred term seemed to be "aboriginal" but my impression is that lately the preference leans towards "indigenous".
Both of these derived from Latin and would therefore have presumably been accessible to any educated person in the 19th century. In contemporary Canadian French, the term autochtone (derived from Greek) serves a similar role.
Note that "First Nations" is disqualified for two reasons: first and most importantly, it is a legal term which is explicitly not inclusive of Inuit and Métis, and probably fails your criterion #2.
I don't think the problems with "Indian" need restating. The word "native" on linguistic grounds would seem suitable and AFAIK was the preferred neutral term as recently as a couple decades ago (and is still used that way by many Canadians without intended offence) but in political speech it's become tainted and could be interpreted as pejorative.