I'd try sawing one of the suspects in half longitudinally, file the edges clean, then look under magnification for thinning in this region, to positively confirm that this is a problem. The paperclip test is all very well, but can be falsely reassuring. Certainly if you can feel a groove with it, the cases are unsafe.
I agree that, if you are FL sizing you may be pushing the shoulder too far back compared with your rifle's chamber dimension.
Your rifle might even have excessive headspace. If possible ask a gunsmith to check it with go/nogo gauges. If it turns out to have excessive headspace (closes on nogo gauge), consult the gunsmith.
During firing the case obturates and grips the chamber very tightly. The only part that can stretch is that ring just above the case head, which it will do, until the head contacts the bolt face. This thins it out at that ring, and also means the overall case length grows. If frequent trimming is required it is a strong indication that the cases are being "stretched" just above the head.
The more usual case "stretching" requiring only occasional trimming is a different mechanism, where brass flows forwards from elsewhere in the case body.
For this to happen in only three firings is worrying. 30-06 brass should last many firings before head separation warning signs become obvious, like this. Or it could simply be that the brass is of poor quality.
You can check this scientifically using callipers and a body comparator, or, almost equally as well by using a roll of 3M Scotch Magic tape, which is approx. 0.0025" thick.
First measure headspace on an unfired case. Do this by first measuring the case OAL, from the head to the end of the neck.
Then add the tape, one layer at a time, to the case head, chambering the case each time, until the bolt becomes a little stiff to close. You don't need to remove the firing pin unless you are doing this with live rounds, for safety, it doesn't stick out until the rifle is fired. Now measure the case OAL with the layers of tape stuck on the head. The increase in length is the headspace of your unfired cases in your chamber. My suspicion is that this is quite large. Also divide this figure by the number of layers of tape, to "calibrate" the thickness of a single layer of your chosen tape. I do recommend Magic Tape as being very consistent and incompressible.
On first firing the case will stretch, in a ring just above the head, by roughly this amount. You can't avoid this on first firing, but you can reduce it on subsequent firings by adjusting your sizing die so that it only bumps the shoulder back by a minimal amount, say 2-3 thou.
Again, the tape method lets you do this in a controlled way. Back the die out a bit, say half a turn, resize a fired case, test in rifle chamber, it should not fit, stiff or impossible to close bolt. Wind the die in, bit by bit, resizing and testing the case in the rifle each time, until the bolt will close without resistance. Now add 1 layer of tape (2.5 thou, or whatever your "calibrated" tape thickness is). Bolt should still close without resistance. Now add a second layer of tape, i.e. 5 thou total. The bolt should now be stiff to close, if you have got the die set just right. Lock the lock ring (you'll need a locking type, not e.g. the Lee o-ring friction things).
The thread on a die is 14 threads per inch, i.e. 1 turn = 71/1000" 1/8 turn is 9/1000", so the adjustment needed is very fine, but it can be done surprisingly accurately, with a little finesse.
Test all your resized but unloaded cases in the rifle first for function, before loading them up. From now on, all being well, you have got your die set and locked. For your rifle, in your press, with the specific shellholder that you used. Change any of these things and you'll have to at least repeat the tape test, or re-adjust.
Sounds a palaver, but really it isn't.
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