Tight kingpins will not help at all. A bushing should not be crushed it has to have room to flex. The pivot on the hanger could be a bit tight in the pivot bush in the baseplate and you could try lubricating that, try rubbing soap from a soap bar on the pivot on the hanger. If it fits to tightly in the pivot bushing then change that. Get a hard not soft pivot bushing.
Very hard bushes and a lot of normal bushes don't have much rebound and won't return to centre no matter what you do.
If you are still having trouble then change trucks to a well known brand (eg Independent) or just don't worry about it and just skate can't really see why this would really make a difference to using a skateboard, as you say it straightens out when you apply opposite pressure. Don't let it bother you.
Learn to use loose trucks, because loose trucks save lives....
