We got our Pakistani visa in Tashkent, Uzbekistan last September. The embassy gave us the same line we have heard before, "you have to get the visa in your home country". We explained that the typical 6 month validity of the visa would have expired prior to us entering Pakistan, so we couldn't get it prior to leaving.
The embassy staff in Tashkent was understanding and granted us the visa. The embassies still have latitude to give you the visa outside your home country, if they choose to. We tried in Ankara and Baku and they would not help us.
If you are not travelling on an Israeli passport, maybe you could send the passports to the Pakistani embassy in the country where the passport is issued? You can't enter Pakistan on an Israeli passport, can you???
The Pakistani embassies have been a real pain in the a** with this "home country" stuff, but with persistence you can probably get it. Just make sure you have a few other embassies you can visit as a backup, we visited 3 Pakistani embassies before they issued us a visa.