I have been promised the date of 22 July. Everything did go amazingly smoothly on 15 July. One amazing instance in which the tatkaal form counter was about to close at 12:00 pm and I was there exactly as the time turned 12:00 pm. If I was a minute late I would have had to come back next day.
I suspect the long delays are caused by the staff being directed towards the new Passport Seva Project issuing the quick e-passports. They are so very eager to make the new project a success that a 3-month delay over the official 45-day time period for the older applicants is just not an issue.
Anyway, I am glad they pushed forward my application without extra charge.