May be a new thread would be helpful. Lets try to make the problem smaller.
Headstamps are only regarding to caseform, material, alloy, manufacturing.
Mostly headstamps are stamped and could not be changed while reloading ect.,
So any info about charge or projectile would be rubber stamped or painted - so it could be changed or removed easy, if the case would be used several times.
The “F” was only found on “Army” cases? ( or navy and projectiles, primers too)
If we know - only army - only cases - thats a step.
Are there any cases without “F” or other letters?
What is the time frame of “F” cases - only WW.2 ?
Will the “F” be found on steel cases?
If our japanese collectors would be able to have a look at their references or cases to ask these questions?