EA App opens in Windows but its just a blank box. How can I play the games I buy

So, I buy very little from the Origin store. I used to like the Origin store, but now its the EA store. I don't know if its been rebuilt from the ground up, but its terrible. 

But that's not even what my question is about. I'm not going to stand around and wait for EA to fix a simple game purchasing gateway that is preventing me from playing the games I've paid really good money for. No!

My question is simple - these games are available on Steam - How do I transfer my purchases to Steam without repurchasing them? There's nothing wrong with the games, the problem is the EA app DRM or failures in the App UI interface that prevent me from playing the games I've paid for. Its that simple. Steam works. Gog works. EA occasionally works. UPlay is a god-awful disaster and I think Ubisoft want to be the new EA. And to be fair, the games I want aren't EA games, they are Westwood games. And the other massive property I love is Origin games, which are also not EA games but was the name of the portal I bought these games through. 

So, Its not as if I'm asking for you to fix your service. And as I've pointed out, this wasn't the service I purchased the games through, but both services were owned by EA and EA has clearly admitted defeat and sells these games through Steam now, so could you please transfer my licenses to my Steam account.