The more I think about it, the more an even more rational version of a HP-fanfic should be called "Harry Potter and the Time Turners". Probably less entertaining, but that's the downside when you take your characters' intellect seriously ...

Eliezer has said somewhere that if Harry were written as a perfect rationalist, he would be too ridiculously super-powerful for an interesting story in that universe to be possible. Harry is simply at the level he is, and it is not really a fault in him or the story that he is not further advanced along the path than he is.