Yosemite to El Capitan
After more research and other similar questions on Stack Exchange, I have come to the solution I was originally looking for.

This website provides some instructions, but more importantly direct links to the .pkg files for El Capitan on the osxapps.itunes.apple.com domain. You can then use the checksums from this git repo to verify the installers if you still feel something is fishy.

I also spent about an hour on webchat with Apple support trying to get El Cap added to my purchase history for my Apple ID, so I could just download it from the App Store, to no avail. Their official recommendation was to find it on a third party site. Couldn't believe it. They also noted that going into an Apple Store / Genius Bar may yield results with getting it installed (or any Apple Authorized store), at which point backup media could be created if it ever needed to be reinstalled.