Try to sit as far up front as you can. First one off the plane makes a huge diference , I've taken the jumpseat versus a back row just for this very reason.
I've made way tighter connections as had the crew call ops to see if they were listening (outbound flight) just to tel them your coming and not leave early if at all possible .
Lots of the guys I've flown with do the walk to make sure we leave no one behind .