Ohhhh, the plot thickens then. Looks like I found bad data for the 360NE. But everything on the internet is supposed to be true! =:3

Referencing the CIP drawings for each cartridge:
https://bobp.cip-bobp.org/uploads/tdcc/tab-ii/8-x-57-ir-en.pdf
https://bobp.cip-bobp.org/uploads/tdcc/tab-ii/tabiical-en-page33.pdf

It looks like the 8x57JR rim is ~.524, while the R360 is ~.488 as you say. This thing is definitely larger than .488.

But it was my shotgun ammunition that arrived today. The 8x57JR brass and the 16ga load-all conversion parts are tomorrow. Aaaaah, the wait!

I did do some "function testing" (chores, chores) on the shotgun barrels, though. Hoooo boy those clays were poofing.

Carefully posed ammo pr0n shot, including some ridiculously expensive properly-headstamped .32-40 Ballard that I can't shoot and reload with the Holy Black until I fix that other gun. Grumble.