In our house, DD would never have read math stories by choice, whereas DS actively seeks them out. Reading the stories may reflect natural interest rather than a reflection of talent. DD really enjoys math now, but I would never have known it from the stories she read when she was younger.
The teach the kids yourself through middle school approach will work fine unless you are talking about competitive math contests. Even though I have a Master's degree in engineering, I think that when it comes to competitive math contests, the professionals are better (e.g. Russian Math or AOPS) even when it comes to middle school level teaching. They just have a grasp on techniques that are proven to work. If cost is an issue, Khan Academy can be a useful free supplement prior to the paid lessons.
Even when it comes to a university tutor, I would be very selective. There can be many tutors who understand the material well but are not able to teach bright young children.
