my 8mm mauser rims are at .469.
the spec for your 8mm Mauser rims is .473" and the spec for the case head is .470"
The spec for the 6.5x55 Swede rim is .480" and also for the case head. The Swede case is not the exact same case as the other Mausers, (7 & 8x57mm)
Now, you've measured, and you see that the ACTUAL diameter of factory ammo is a little less than the spec. This is intentional, as #1, the listed specs are maximum dimensions, and #2, so the ammo will work though guns that are not at maximum dimensions
I have used R-P brass (though I don't have any available to measure right now, I'm told its the "standard" .473/.470 rim/head diameter.
it works just fine through my 1917 dated M96 long rifle and also works through my 1897 Norwegian Krag. At the industry standard max pressure of 45,000psi, the slightly smaller American brass doesn't give ME any issues.
If you're going to hot rod the Swede, and in a suitably strong rifle, push it to 50-55,000 or higher, I would recommend using the closest match between your chamber and your brass possible.
ALSO, mark the rounds (sharpie or something) so you can determine at a glance if you are loading over standard pressure loads.
The Swede is a great cartridge, delivering flatter trajectories than similar weight bullets in the .30-06, and enough energy to get the job done, even on beasts the size of moose.
120 and 140gr are the most popular, but don't overlook the effectiveness of the long 160gr RNs. The Swede "military" load with a soft point bullet is a great penetrator, and gets the job done in workmanship fashion.
Ammo availability has been mentioned, and its true, not every Walmart will carry the Swede. So what?