The accuracy of a strain gauge on your rifle cannot be calculated, as you can not accurately measure the location of the bonding, the orientation of the bonding, or the quality of the bonding.
The formula for a threaded and screwed barrel pressure vs strain in not in Roark's book.
The math would be impossibly difficult.
If you use calibration ammo, you must find it's traceability to NIST and it's inaccuracy. Plus there is the error when shot in your chamber, which cannot be quantified.
A measurement of unknown accuracy has no value.
Finally if you did have an accurate measurement of peak psi in your chamber, what would you do with it?
To have meaning you must compare it to something.
You might say SAAMI registered peak average pressures, but how those were chosen is demonstrably capricious.
In the strong action the real question is threshold of brass life.
You have the answer in your hand, and to purse a strain gauge option is taking leave of the senses.
Sure, if you are going to sell ammo for the wide variety of guns it may be used in, you must have a pressure standard. Ballisticians have traditionally shipped ammo back and forth to get consensus, and did not have calibrators traceable to NIST.
But for the individual handloader, loading his own ammo, he has direct access to the goal information, what is the threshold of long brass life.
How did the Germans get 2900 fps 150 gr 8x57mm in 1905?
It was not based on how strong the actions were, it was based on the strength of the Mauser case head.
Try to make one of those old Mausers go faster than 2900 fps, and you will see that it is already up against the threshold of long brass life.
Many years later SAAMI may have registered that kind of pressure for the Mauser case head in the 270, but they did not for the 8mm.
So if you had a strain gauge on an 8mm what is your goal pressure?
You would not want to feel stupid for buying it so you would have to play with it somehow.
Maybe workup a load to the threshold of long brass life, and then measure that pressure.
You could then say that pressure is your goal.
Kind of like shooting arrows into the fence and then painting a bullseye around them.