Well, I'm not that concerned anymore, but I'm posting this in case anyone else is worried about static electricity around their iPad. I was reading about the aluminium casing of the iPad and grounding and got the idea that the coat might just have reacted to having the aluminium nearby, and not have shocked the connector directly. I didn't see it happen, after all. If this is the case, the casing is actively protecting the iPad from static shocks by grounding the user to it every time he picks it up, or so goes my theory.
In any event, I'd taken to holding the iPad sideways, concerned about the jacks on both sides, and thought I might try a "safe" experiment wearing that same long coat. Lo and behold, I slowly bring the iPad, but neither socket, close to it (screen on, in active use) and hear a light, ongoing crackling, if I heard correctly coming from the coat close to the ground, not from anywhere near the iPad. While I'm not exactly sure what this means, it does tell me that the aluminium hull of the iPad seems to be what it's reacting to and would support my thesis that it's protecting the iPad. That, or it's the screen. Either way, I saw no noticeable effect to the iPad either time, no interruption of what it was doing, no reduction in performance (using a performance testing app), no screen blip, nothing.
I'll probably ground myself a lot more often in the future when an easy chance presents itself (door handle, &c.), but I have no reason to believe anymore that static electricity is a major threat to an intact iPad, and am 95% certain mine is fine. Still, if someone has anything to say about their experience with static I'd like to hear it.