While the process may not be expeditious and a bit more onerous, the Government of Pakistan does grant transit visas to Indian Nationals, as your very link points out. Note that a transit visa does allow a brief visit to the arrival city, but does not require a sponsor. Only a business visa mentions that a one is necessary, nor you would not be requesting a visitor visa.
VISA POLICY (for INDIAN NATIONALS)
All Indians wishing to visit Pakistan must obtain a valid visa. The basic requirements for obtaining a visa are as follows:-
i Valid passport: The passport should be valid for at least one year.
ii Visa application form duly filled in.
iii Visa Application forms for getting visa's either through the Interior Division or Pakistan Mission abroad.
The fee at present is Rs.15/- inclusive of all charges for issuance, extension or transit visas.
Transit visa valid for up to two entries for stay in the city/port of entry for 72 hours issued to Indian nationals, proceeding to Indian by air or sea through Pakistan.
Following are the designated entry/exit check posts for Indian nationals, coming to Pakistan:-
i By Air Karachi/Lahore/Islamabad.
ii By Sea Karachi.
iii By Road Wagha.
Instruction for Obtaining Pakistani Visa
i Please fill in the visa Application Form in CAPITAL LETTERS (Four copies). No column to be left blank.
ii Please fill in the Computer Performa in CAPITAL LETTERS (Four Copies).
iii Visa fee of Rs.15/- should be deposited in cash and receipt obtained.
Passport will be returned on presentation of receipt. The fee is non-refundable.
iv Two copies of the form will be returned to the applicant with visa. One each should be handed over to Pakistan Immigration Officer on arrival and Police Registration Office.
v The applicant should be in possession of US $45 or equivalent in Foreign Exchange at the time of entry.
vi The visitors may enter Pakistan by Air, Train, Road. but the point of exit and mode of travel for their return journey will remain the same. However, the persons Entering By Air may exit from different Airport with Prior permission.
vii The visitors must Report for Police Registration within 24 hours of entry in Pakistan and prior to Departure/Arrival at each subsequent place of visit in Pakistan.
viii Provide copy of N.I.C of the sponsor of Indian National(s).
ix Provide copy of the Passport of the applicant(s).
x Valid Passport. The Passport should be valid for at least one year.