@Bluebellflora
Ah. That makes sense. I'll put that at the bottom of my buy list. Lol.
Sorry if I was over-explaining user accounts. I figured you knew, but you never know where people will get lost!
So, here's the most recent update. I deleted the cookies while I had everything installed that I mentioned in the previous post. From my CPUGenuis account I used the Sims 3 uninstaller and renamed my EA documents folder to save my saves. After everything was uninstalled using the official uninstaller I opened up Origin and everything behaved as expected! It said that those EPs were uninstalled and ready for downloading from the master profile!
I'm not sure if it was deleting the cookies or some weird product registration error. It was probably a combination of both held by the information in the cookie. This makes sense to me since the Sims 3 download page in the Origin app acts and responds like it was coded with HTML. I'm guessing the EP04 cookie went stale (lol) when I deleted the game without using the installer initially. It then added a base game cookie but kept reading the newer EP cookie.
At least, that is my best guess. It is still a very interesting bug. Either way, everything is now running as expected!
And it is my pleasure to keep providing feedback. I know that the game is no longer officially updated, so the best way to help the game community going is to help people fix bugs before they start. I was honestly elated when I saw that there was somebody on the forums running precise and concise guides for fixing problems. The help that you've provided has been much appreciated.