I'll post some observations here, too, as my I and S test toward the middle; the MBTI we took in a career development class a couple of years ago gave me ENFP.
I've got that same 'calm in an emergency' trait. I don't panic -- just observe and take action.
In a mixed discussion group I'm in, where people tend to jump in, I take notes (the only person out of about 15 who does) and often don't talk until maybe two thirds of the way through. One time after the meeting someone approached me and asked if I'm a teacher (no) because I have a "gift for synthesis."
I don't how these traits relate to MBTI, but I thought I'd add to the voices saying you're certainly not alone.