Hi Paolo, and welcome to the HUBB
As for personal experience: since 2010 you can only apply for a pak visa in your own homecountry, unless you're resident in the country you're attempting to apply for it, at least since six months.
It has happened to me on 2010, when i was in Tashkent heading to China.
We were on struggle to send back our passports to Italy, tryng to apply over there, but we're in a hurry due to a meeting point at Torugart to get to China.
We took the "risk" to reach Sost border post and we were "lucky" to get it there.
I do not know if you are on a such time schedule, otherwise you can consider to courier the passports back to Italy to be processed (i can't swear for any guarantee).
...hope to get wrong myself.