It worked twice for me, but it wasn't really easy figuring out how to proceed for it to work.

I did a test install on another computer before attempting anything with my main computer.
Just like you, I had the installers for every game I purchased through Origin, and I had backed them up on a USB storage device.
I also had almost every single patch in a back-up drive, so I installed everything in order, patching when necessary.

When it was time to install what I had purchased from Origin, I tried doing the installation from the desktop and the installer was placing the files in the EA folder, but when I tried to patch for that expansion I just installed, the game refused to do it. So I started over, still on that testing computer, but I created a folder that was called Origin Games, just like the settings in my main computer where the game is working, and I placed the whole expansion folder in that Origin Games folder, and ran the installation from there.
When it came to the point where the game is asking if I want to install somewhere else than the EA folder path, I linked it to the folder of the actual expansion I was installing in the Origin Games folder instead, and from what I saw, I believe the installer overwrote what was already inside and proceeded with the installation. Patching for that expansion worked by proceeding this way.
So I did the same for every expansion that was originally installed in the Origin Games folder, and then I patched to 1.67. I made a copy of my actual game folders and tried to start the game and it worked perfectly fine.

I proceeded the same when the time came to reinstall on my main computer, and it seems to be working the way it's suppose to.
I must say, once in a while, the game doesn't want to start from the first try and I get an error message, but it always end up starting anyway, with nothing missing.

During the installation process, I didn't install Origin or EA download manager. But it seems that I really had to place the expansions I bought online in that Origin Game folder I had to create to make my game playable.
Maybe because you bought some of your expansions on Amazon is the reason why it worked on your end when installing in the EA folder. Or maybe if I had dropped everything that was in the Origin Games folder in the Electronic Arts folder instead, it would also have worked...
It's only speculations, and it wasn't simple to figure out, so I can understand igazor's warning.