Well, there is a contradiction if ever I saw one. Swapping dependency on one for dependency on another imho. To be truely independent, Pakistan cannot bend to any particular major power. That means either keep all at bay, or cement relations with all (thus counterbalancing different dependencies).
CSOCs high performance frigate appears armed with HHQ16, which gives a range of 50km at best, which is comperable to ESSM, of which you can load 32 into a single 8-round launcher. I'm not so sure what advantage CSOC's HPF would offer PN over an improved F22P (which could be built by CSOC as well as Karachi shipyard).