Now bare in mind I was alone and was kicking dirt when I drove but did make plenty of stops for rest. It really should not take you more than 7 - 8 hours at most from Naran to Astor.
Now I do agree with your friends in that there is a 12 hour drive but that is from Islamabad to Chillas via the KK Highway. I would choose the route of Naran, Babusar Pass down to Chillas and then carrying on to Astor. The reason I would prefer this route is that if you choose the KK Highway you will be driving pretty much the full 12 - 14 hours in heat where you may get occasional cool temps but mostly in heat. Whereas if you take the Babusar Pass the heat will be for perhaps an hour on this side and another two, maybe three hours on the other side of the Mountain on the KK Highway. Just carry plenty of water along the way, plenty of Cool Water. Or have a thermos full of ice so you can mix the water since your water bottles will heat up pretty darn quick on KK highway.