This isn't necessarily a "competition" that anyone has to lose. Harry could always take a third option and attempt to make a rationalist polyhack on the problem. He's shown the ability to get along well magically with more than one different person and it doesn't seem likely that he would distance himself from one if history had shown he could use their help for important tasks. Also, my understanding is that Harry hates disappointing people. Considering that, it's a little hard to imagine him turning down Tracy without at least considering a way to keep them both her and Hermione happy simultaneously. It would also come in handy in the future if the story extends long enough for him to meet Luna Lovegood.

And the fact that I think this would be an idea that I would really like to read now that I have thought of it seems like pretty good evidence that I am shipping.