A likely explanation is that you need to wind down the sizing die a bit more.
My experience (7mm 08) is that it took 3 or 4 loads before a few of my cases started getting tight to chamber. I had set the die to reach down to just touch the shell holder then loosened it off 1/4 turn. Wrong move ! in fact I needed to tighten it up a quarter turn beyond where it bottomed out. The press stretches a little as it compresses the case. Once I did this the cases fit easily and continued to fit for another 10 firings.
To measure how far the die is sizing the case you need to measure the length from a "datum" on the shoulder to the base. As well as calipers, you need a ring of standard diameter (.400" for .308 win family)which sits on the shoulder. At the other end, it helps to have a flat "anvil base" to fit onto the caliper arm. This base to shoulder-datum length is called the case headspace dimension to distinguish it from the chamber headspace dimension.
Most full length dies only size the body down to about 2-3 mm from the base (as vartarg says). This is because the case body only stretches (expands) for the front part. The base, often reinforced a bit, seldom expands unless pressures are really excessive. In that situation, the primer pocket also stretches and the primers fall out . So, it's unlikely your base diameter has stretched beyond SAAMI specs. When working up loads some people will measure this base diameter just above the rim and below the shiny line and if it increases more than 0.001" its a sign the load is too hot (IMHO, that piece of brass is dodgy afterwards). Also, as you fire the and resize the case several times, the junction between where its restretched and resized down and the unstretched unsized base gets work hardened, thinned and appears as a bright ring. Eventually it will separate there. You can feel the thinning on the inside with a paperclip, also as as described by VARTARG. However, all reloaded cases show some shininess there, about 2mm above the base and it doesn't mean they are about to separate or need to be chucked away.
My experience is with 7mm08 and milder cartridges I understand the 7mm SAUM is a different kettle of fish so will be interested to hear from 7mmsaum what he finds with your cases.
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