"to counter the extremist narrative ...
In my inexpert view (I've never met an extremist, and would probably just think: nutter, if I ever did) it seems that the best way to neutralise the views they hold, is to make "our" stories better than theirs.
If you spend a large amount of your formative youth hearing about how bad the west is, how morally bankrupt we all are and that our whole society is venal, ungodly and otherwise damned - then the best defence would be a charm offensive instead of confirming their worst fears by raining down firey death on anything that happens to bear a passing resemblance to the CIA's Most Wanted list.
Maybe our lot should be out there with stories about how caring we are, how we all love small furry animals and our mothers. That we have a highly charitable society that doesn't want to screw over the rest of the world and that, best of all, we'll open some Pizza Express and Starbucks in their towns, too. Maybe even a Hooters in their capitals? So that their leaders can "know thine enemy"?
Then, once their children can see all the good things we have to offer, just like their communist counterparts did a generation ago, all the hate, fear and insecurity will evaporate. Instead of bombing the crap out of their villages, we'll parachute in washing machines, Playboy, waffle-makers and icecream instead.
Make them just as dumb, fat and happy as the rest of us.