Well, the priority date here isn't of much value.
For someone who is applying before the 3/5 year anniversary:
If the background checks are completed, then can only schedule an interview no more than 30 days before from the date you become eligible for naturalization (3/5yr anniversary). That is the reason you will see "in-line for interviewing" exactly a month (+ or - 2 days accounting for weekends) from the anniversary date, if you have done your biometrics and FBI/IBIS checks are completed.
In a nutshell, some one who has applied 3 months ago but is 45 days from the anniversary date will not be scheduled, but the one who is say past her anniversary date and applied 2 months ago, will get scheduled earlier. They may schedule as soon she is placed "in-line" like mine or later, based on the load of the field office (which varies).
Once the case is handed off by NBC to the FO, your timelines are all dependent on the FO