Thing is, Amazon was not one of the three. And I always thought that Amazon would be the perfect daddy for my baby.
So after the first three companies were looking at my books with NDAs and LOIs, I asked a connected friend to introduce me to someone at Amazon, and told him why. I was surprised how quickly someone at Amazon got back to me, and they were a contender until the end. (I chose a different company - one of those first three, after all.)
It makes all the difference in the world to have multiple interested buyers.
Any time you hit a snag in negotiations, you really have to be 100% sincerely ready to walk away. Actually believe, to the core, that until the final signature and wire transfer goes through, the deal might not happen, and you're OK with that.