It seems to me that somewhere it says he had to make a river flow backward, or make rain fall on a sunny day, and something about having to explain some 300 reasons why something is pure and then another 300 for why it is impure… Am I in the right area, or am I just imagining things??

I don’t deal with aggadic literature. Maybe there is some aggadic passage like that, but that certainly was not the accepted procedure for ordination. It is written, though, that for appointment to the Sanhedrin one had to present 150 reasons to declare a creeping creature pure (but that is a non-halakhic, non-binding description).