There is a big difference in how much the OAL is after sizing and where the case shoulder is.
None of us have the rifle and cases in our hands and the OP is even being told to take the rifle to a gunsmith and check the headspace.
SAAMI headspace on their chamber and cartridge drawings is listed as min and max. And there is .010 between the min and max tolerances. And GO and NO-GO gauges have .003 between them and are used to set up new rifles or re-barreled rifles.
Chambers and die vary in size and the OP might have a large chamber and a resizing die on the small side. Meaning this would explain why his OAL case length after resizing the case.
I'm 67 and have been reloading for over 47 years and have never just neck sized a case until it has resistance closing the bolt and then switch to full length resizing. Bottom line, keep it simple and bump the shoulder back .001 or .002 after measuring a fired case. The third time I neck sized a 30-06 case in a Remington 760 pump the case would not eject until the case cooled off a few minutes later. So what is gained by firing a case 2 or 3 times to find out when the bolt is hard to close.
So far the OP has been given some bad advice, a new case has been annealed and the case shoulder and neck are soft. And yes the case shoulder will spring from its fired size and a resized case shoulder will spring back from its resized location. And you are talking about a few thousandths of an inch and the OP is measuring the fired case and not guessing where the case shoulder is at.
Thousands of reloaders just use a Wilson type case gauge to measure the "resized" case and never have a problem. And the OP has a Hornady cartridge case headspace gauge and is measuring the "fired" case length and is more precise than a Wilson type gauge.
Now look at the chart below that I posted before, and read the chart at what point the case started to stretch. These cases did not start to stretch until the 7th firing, meaning the sizing die was a close match to the rifles chamber.
Bottom line the OP needs to do some more checking and measuring, but the OP doesn't need to start neck sizing or take the rifle to a gunsmith.