I went to Harbor Freight and bought a 1" micrometer, the Fed GMM primers mic'd to spec. 0.2111.
I then pounded some scrap lead (recovered 22 rimfire bullet) into the primer pocket of a bag fresh 6.5x55 Swede casing, and it mic'd slightly larger, 0.2150. I may have enlarged that number a tad by pushing the lead back out of the primer pocket with a universal depriming die.
I then took the primer I measured and used the Lee hand seating tool to seat it, and it went in with what I would call "normal" resistance. About the same as a CCI 200 or BR2.
Unfortunately I had already primed all 50 of the new 308 Brass (which is why I had to open the bag of 6.5)
So I guess if you encounter Winchester brass with tight primer pockets it might not just be me.
Machine guns are awesome until you have to carry one.