If I use the GSC method I should be able to get a case sized to the actual specs of my chamber. Then, if I were to compare that to SAAMI specs, I should be able to calculate the difference in my own chamber.

Its is so to say a way of finding out if you need to or not have measurements done professionally.

Purchase the right gauges and measuring instruments and learn how to use them
No need for "professionals"

If I use the GSC method I should be able to get a case sized to the actual specs of my chamber. Then, if I were to compare that to SAAMI specs, I should be able to calculate the difference in my own chamber.

A case sized - and or fired in your rifle chamber will always be slightly smaller than the actual chamber
It needs to spring back enough to be able to be extracted.
The ONLY real way to know what is going on in your rifle chamber is to cast it using cerrosafe or similar low melting point alloy

https://www.youtube.com/watch?v=OG1-J-P0IoY

https://www.youtube.com/watch?v=voMp0IQwDLU

Making a chamber casting

Cerrosafe

Unfortunately no-one has been able to tell me where to get this in SA ?

SAAMI chamber print can be found here

American National Standards Published by SAAMI

CIP chamber print can be found here

COMMISSION INTERNATIONALE PERMANENTE POUR L'EPREUVE DES ARMES A FEU PORTATIVES

All sorts of different .308 reamers can be found here

4D Reamer rentals

All you have to do is learn how to read a chamber print

You can make chamber casts from flowers of sulphur. Thanks what most smiths used in the olden days. It stinks to hell but I've seen casts made using it and they look excellent.

I know an old gunsmith who told me how to make a wax chamber cast. It takes time and effort, but is accurate enough to get the necessary specs.

Here is another mehod to give a "close enough" measurement.

Size 5 cases to minimum, trim to minimum spec, load a moderate charge and shoot them in a clean chamber. Now compare case length before and after firing.

Its is so to say a way of finding out if you need to or not have measurements done professionally.

Purchase the right gauges and measuring instruments and learn how to use them
No need for "professionals"

*****************************
Any idea what this would cost for 8-9 calibers, just as a once of use, to get a once off answer, even for just an answer on this one rifle once off ?

These may be part of what you need
https://safarioutdoor.co.za/catalogsearch/result/?q=Chamber+Length+Gauges

here's how to make your own way
https://bulletin.accurateshooter.com/2018/03/how-to-craft-your-own-chamber-length-gauge/

Cleverrrrrrrrrrrr ! I never thought of that myself

https://www.google.co.za/search?q=headspace+measuring+tool&sca_esv=4771c1dce5b9df5f&hl=en-ZA&sxsrf=ADLYWIJyj_JQcSmeioN5sxCRiWr5neNGhQ%3A1715629200927&ei=kGxCZpCEOICJ9u8PidSfoAI&oq=measuring+headspace&gs_lp=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-&sclient=gws-wiz-serp#fpstate=ive&vld=cid:2e4578e9,vid:riVRHOog69g,st:0

To measure the case length to the shoulder, you need some tools that actually index on the case shoulder or "datum line".  These cost money.

A cheap trick to get similar results is to use a sized 9mmP case.  Stick it over the 308 case mouth and measure from 308 base to 9mm base.  The exact measurement on a fired case, a new case and a "bumped" case will usually tell you the story.

The "datum" shoulder diameter is .400". A.40 calibre or 10mm case might work better.

All these tools are comparators. Comparing one case to another. If you have a "zero" headspace gauge, you can then compare it to your case size.

Easiest is dtil to take the rifle to a gunsmith and ask him to measure the headspace.