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I have reamed hundreds sorry thats the wrong description de burred hundreds of GGG cases in 308/7.62 over the years and never had a problem I suspect you are cutting the the primer pocket deeper than it should be.
I use a LE.Wilson trimmer with a LE.Wilson primer pocket trimmer with out any issues. If you are binning the cases I would take them of your hands. But before you atempt to remove the crimp.

You do not need to ream the primer pockets you just need to remove the crimp. It takes no time at all.

My method of de-priming and removing the primer crimp from Berdan cases using a Lee chamfer tool and pin.

Looks like it was sh1te on the firing pin after all, this is one of 5 cases that I just set the primer off to annoy the wife and gee up the lab!
One thing it's worth pointing out is that the primers actually moved back to just proud of the case head by a midges dick, but they all went bang.

Primer movement is common in low or no (as in this case) pressure firings.

I’ve tried removing the crimp on GGG 7.62 and 5.56 with both a chamfering tool and an actual proper RCBS primer swager tool and although both are quick and easy and both get the job done I prefer the chamfering method, only thing I will say is that the proper tool is more consistent, I did find seating primers a little harder though