I can access my full ME3, including DLC, via EA Play app with it (can also still play via Origin).
Don't know if they've since switched EA Play all to this new (crippled) EA Play desktop app.
At least that's how I did it 2 months ago. If you can score one of those, you'll be able to get the DLC through Origin client. I also made an alt with a cheap 1-month EA Play sub. And why they need yet another app, I don't know. To be fair, the EA Desktop app is called a 'Beta'.
