This is an event that I've thought of too, especially because it's a trope for fanfiction and each writer does it differently. I do think there is the possibility that Hermione and he could find their way to being friends faster if Ron wasn't involved since most of the aggravation with her stemmed from Ron in the first book I believe. I think that Harry would be more willing to giver her a chance since she would be an outcast just like him.

Laura//Hufflepuff