How to propose collaboration, when I have an idea for analyzing another group's data?
I would contact the postdoc you previously talked with. He could be senior enough to run the whole collaboration without keeping his supervisor in the loop all the time. At the very least he has close access to the supervisor, and would prevent you from "cold-calling" the PI with your idea. Why try that again when you already have a contact? This is of course assuming the talk went well and you think he would be welcoming the collaboration. 

About how to suggest it: Don't tell them that your method is better than theirs. You could tell them you have an alternative idea that might give better results. As far as you could test it, this seems to be the case and you'd like to try it out with more data, preferentially in the form of a collaboration. This avoids telling them you're better than them / they're wrong. Nobody wants to hear that, and in this case they also don't need to hear it.