The repeatable but frustrating workaround for launching Anthem mentioned previously in this thread mostly still works. Install a full version of Origin 10.5.78, uncheck all of the install option except the Terms and Conditions, and launch it when the installer prompts. After signing in Origin just displays a "Please use EA App to continue" error screen which you should leave up. Launch the game through Anthem.exe directly, the Origin window should minimize, and the game will launch. Unfortunately, closing Origin will cause the application to attempt to update, and Origin will need uninstalled and reinstalled to launch again. EA App doesn't need uninstalled, but both can't be running at the same time.
This is not a solution to the core problem, however; I am able to confirm that my EA App specifies that I have the Legion of Dawn edition in the game info plate, but the DLC in the EA app doesn't have an owned tag next to it (if it should), and I had an Origin Access membership at the time of Anthem's launch. As I am able to check with this workaround, whenever I look at the Rewards page in game it doesn't show the Legion of Dawn items there.
I was a little surprised by the number of other people I encountered this morning, and I hope a few more of us can return to Bastion soon.
Thank you, and I'm sorry, to the Sunken Cell Event group I was in when my PC crashed. One problem at a time.