What interests me is what made people like Grace and Rose so special to him, when none of his prior human companions got to him that way?
I disagree with this, I think he felt equally strongly about many of his past companions, it's just that the nature of the show didn't allow those feelings to be shown in the same way. He certainly loved Susan (albeit in a very different way to Rose!) and I would be prepared to make the case that the Second Doctor and Jamie had a very special bond, although again not in a sexual way.
The Third Doctor was extremely close to Jo, and certainly didn't treat Sarah Jane with anywhere like the same level of affection. However, the Fourth Doctor with Sarah "No, don't you forget me" Jane was upset at her departure, and at the risk of breaking the fourth wall, was hugely in love with the equally bohemian Romana II. The next two incarnations didn't really have a similar relationship (the Fifth Doctor and Tegan? I don't think so) although if you go non-canon for a moment, the Sixth Doctor and Evelyn are often like an old married couple.
Being in love doesn't necessarily have a sexual connotation - I think the Doctor has loved lots of his companions, just hasn't had any wish to go to bed with them. His very need to have companions is a sign he needs that friendship.