‘Progessive history’ focuses more on an individual person’s success and creations, which can have numerous forces affecting the outcome, like personal matters, other technological advancements, etc.
‘Paradigm shift history’ seems more exploratory, or a ‘question everything’ sort of method. No outside forces can touch it. When I think of this model, I really think of astronomy, as there are no true rules into studying the stars and planets, and we as people cannot force the stars to do anything.
Ecosystem theory is like a web model of history – everything is somehow connected, and can affect one another, and both social and natural forces may change it.
I believe the discovery of oxygen used the paradigm shift method, as it doesn’t appear he had much outside forces affecting his work. Bourgeois-class patronage seems like the best fit, as Priestly didn’t appear to share much of his work with oxygen until after he discovered it (the other examples don’t reflect this as much).