I can totally relate to the finding balance! DS told me he tells new kids he skipped "because he thinks they should know that if they want to be friends". I do not think it's a bragging issue, more of a, I don't know, defense mechanism, trivia fact, reason for his weirdness (his definition), etc?
I role played if a kid walked up to him & said, Hi, I'm so & so & am the best ball player on my team & play travel. We talked about that sounds kind of odd. Yes, he's smart but it's what he's going to do with that skill that is the important thing. It's very tricky because you don't want to squash their confidence in their abilities or alienate others either.
As far as grade skips & testing, I think testing is good to really determine what you are working with. I'd be hesitant for a double skip too but I have read research that shows kids that skip more than once are actually happier than kids that only skip once. So it's not necessarily a bad thing.
It is very tough to decide a balance between how much you want them to get their needs met vs. not being the extra "weird" kid for needing so many alternative plans.
