Great that we got that out of the way.
Yes, we can. We need to invite a number of popular religious leaders from every major sect across Pakistan into a conference room.
(Popular leader defined as one followed by more than 10% of his sect's mosques - the number of leaders to be invited will be the number that ensures a 3/4 majority of that sect agree; So if Maulana Alif has 20% of Barelvi mosques following him,Maulana Bey has another 35%, and Maulana Tey has another 25%, the three will be enough to have a majority agreement.
Major sect defined as one with more than 1% of the population's support: So, Barelvi, Deobandi, Ahle Hadith, and Shia would be included. The numbers are just rough ideas, we can conduct a proper survey and statistical analysis if needed)
The conference room needs to be locked down completely, and no food is to be allowed through until an agreement is reached. The discussion of any other topic except for one Eid is to be banned. (these steps might not be needed if we can somehow provide incentive to all the scholars)
One solution is to follow a system similar to the Saudis' Umm-al-Qura Calendar- the dates are predicted and a calendar is made, however, any one Muslim's word that he saw the Eid moon is enough to declare Eid in the whole country one day before or after the predicted date.
The problems with this are obvious - there will almost always be someone who wants Eid to be early and will testify even if he never saw the moon.
Another solution is to have one moon sighting committee that decides for the whole country. Another is to appoint a number of committees in each province and have Eid in the whole country if the majority (i.e more than 50%) of committees agrees that it should be Eid on that day.
The scholars can go through the details and pros and cons of each system themselves.
This can be done, and similar things have been done recently (admittedly on a smaller scale):
"ISLAMABAD: All religious sects in the federal capital will pray at the same time from May 1, 2015 and all mosques will call out the Azaan simultaneously.
The committee which made the decision included two clerics from each of the four major sects in the capital- Shia, Barelvi, Deobandi and Ahle Hadith. A member of the committee told Dawn, the major difference in the prayer timings was at Maghrib and the issue was resolved amicably between the committee members."
Obviously, there are some details that need to be handled and potential problems that we need to be prepared for, but this isn't an ideal world. Ideally, all the religious leaders would have everyone's best interest at heart and would do all this by themselves.
So, will you now provide me with some resources, manpower, and the contact details of every major religious leader?