As for Pakistani exit control, as stated earlier you can have them fly to another country like UAE or Qatar, then board a plane to the US.
I'm not sure what "Do I need to backup with an immigration in case of issue at port of entry?" means. As LPRs they cannot be denied entry IF they never signed I-407s. They may be asked to sign I-407s at POE. If so they need to politely refuse (they cannot be legally forced to do so).