I don't know enough about Native Americans to say exactly how I'd go about the equivalent of a Meiji Restoration, but that's what I would attempt.

Then Japanese were much more similar to the Europeans then Native Americans. For starters they had a government. Furthermore, they had developed some institutions that were similar to western institutions, or at least more similar than anything else outside the West.

I'd pass laws mandating compulsory Westernisation,

First you'd need to create a bureaucracy capable of enforcing laws.