Hi Mewzard - I am just chiming in because I also have a kid like yours (minus the love of maths!) From Ruf's book, i guessed him to be a level 3, and he turned out to be high level 4 or potential 5. My DS4 was a "sneak" reader - for the longest time, i knew he could read, but he wouldn't. Occasionally he would slip! Now, he'll read one chapter to us or switch off pages. But he has only once sat down by himself to read a book (and it was calvin and hobbes, to get ideas for mischief!) Now I see more of a difference between him and agemates simply from his advanced vocabulary, but most of the times he just seems like the other kids (except he can read at a very high level and can figure things out). I remember reading the gifted lists in Ruf and thinking, well my kid has zero sensitivity for others, he can't be that gifted. But each kid is different.
Our kids led parallel lives in the early years - we went through a thomas the train and cars movie phase here too. Now it's Lego star wars, lego indiana jones, lego batman (and their related wii counterparts!)
We are worrying about schools now. I agree with the others, that the school situation is unique to each gifted kid. What works for some will not work for others. One thing a good gifted specialist should be able to do is give you specific advice based on your child's personality. But with HG kids, you must at least be aware that if one situation is working out for schooling for one year (or half a year, or a few months), it may not work for the next year. Depending on the kid and the teachers you come across, you might have a great public school experience.
By the way, i think the motivation is what might push you into the level 5 in ruf's book, and this isn't something you can necessarily tell with youngsters who might not have found any particular passion yet. And I think you can be different levels in different areas.