Oddly, Chrome developer tools don't have a "show IP address" option. I say "oddly" because it is a fundamental check that developers do when checking cached items on round-robin DNS servers.
Anyway, via http://superuser.com/questions/633714/how-to-get-remote-ip-in-google-chrome-browser, the ShowIP address plugin / extension https://chrome.google.com/webstore/detail/showip/agoljmemkbciolpigpabjfkagboolkcj gives you the IP address in both IP4 and IP6. They are shown in the bottom right. Whoo.
Unfortunately, this won't help me for the odd edge cache served asset, unless I load only it, which is a little more annoying, but still completely doable.
I prefer Firefox's display of all of the IP address for each asset of the request. Sometimes I'm not working in Firefox.
Regardless, odd problem solved (and I can close that tab! yay!).