I also went to karachi from lahore and back (with family) last month, my car has white lahore licence plate. I was not stopped anywhere in Punjab, but just when i entered sindh, i was stopped by police at every single checkpost. I also had all the documents including the highway code book. but did not had third party insurence. he said it would be chalan of something like 2563 rupees 65 paisa. and with some negotiations, he agreed to let me go if i pay 500 rupees. I then called my uncle who is in Police, he talked to him in sindhi and he allowed me to go. the same thing happened at almost every checkpost.
and on the next checkpost the sipahi said, sir mei qasam kha k kehta hun k iss ka 1600 rupay ka chalan hota hai.
on my way back, I got the 3rd party insurrance made before leaving, but this time they started asking for NOC. I did not know that its needed only to transport the vehicle, so i had to call my uncle again.
but i also gave bribe at a few checkposts thinking i shouldnt be bother my uncle too much.
and they were particularly stopping all the cars with families. regardless of the number plate or anything. and yes, they always ask where are you coming from and where are you going. I always told them that I am traveling between karachi and lahore. and both times, i planned the journey in a way that i cross sindh during daylight, toe shukar hai k daku nahi paRay.