I actually just found a solution over on Reddit that worked for me - feel free to try it out yourself!
The steps, starting with both EA Desktop and Origin closed (you will need both). You will need Origin to know you have some level of DAI on your account; for me that happened by trying to run it from Origin while it was installed through EA Desktop. If you can't do that, you might need to get the pass separately on Origin (6.99?) to get it to work- I didn't need to, but that's what the Redditor said. If you can start it from Origin, these steps should work:
1. Open EA Desktop, download the game, and close EA Desktop.
2. Go to the installation folder (for me, C:/Program Files/Ea Games) and move the entire game installation into the Origin installation folder (for me, C:/Program Files(x86)/Origin Games)
3. Rename the game installation folder something different - for example, "Dragon Age Inquisition Copy" - this stops Origin from automatically detecting it.
4. Open Origin, and tell it to start installing DAI. PAUSE THE DOWNLOAD, and close Origin.
5. In the Origin installation folder, delete the Dragon Age Inquisition folder that Origin just created, and rename the "Dragon Age Inquisition Copy" back to "Dragon Age Inquisition".
6. Restart Origin, and tell it to resume the download, and it will detect the already 'installed' files. For whatever godforsaken reason, there's some file in there that indicates it's SUPPOSED to have Trespasser, so it will download it when it gets to the end of verifying the other files.
After that, I'm playing it from Origin to be safe, but I now see it on the war maps table! Don't forget to disable the awful Origin overlay before playing.
Hopefully this works as well for you all as it did for me.
