Thanks @siddEE.
I just came back from the Chicago consulate. Unfortunately, they did ask for the PPF but I had filled it with whatever info I can find on my and my wife’s passport. My PCC will be delivered today and my wife’s will be sent to the local police station that I mentioned in the PPF. My father has some contacts in that police station, so he will visit them next week to speed up the process and return back the application before the 60 day deadline. If not, then I will use the receipt and medicals as a placeholder to extend the submission deadline. This is the post that suggests that if the Indian PCC does not come before the 60 day deadline: Submit application with a PCC receipt?