How should people facing colonization act to avoid cultural and economic subjugation?

You need either guns or money, preferably both, preferably as much as possible.

suppose you were transported back to America circa 1800 as a respected chieftain

I don't think a single chieftain could change much. But my best bet would be on trying to create a viable country -- probably on lands that the white colonists don't want. Likely outcome -- you die defending it.