Mirror's Edge product key

I'm adding this on "Origin for Mac" because every ME thread has been moved to this subforum, apparently

The problem is as follows: I want to install ME. 96% into the installation, it asks for the serial number. To access the serial number on my EA launcher, I need to click on the 3 dots menu of an already installed game and select "View properties". Before installing the game, it only allows to me install it and manage adddons.

So:

• EA launcher doesn't let me install the game w/o the product key.
• EA launcher refuses to give me the product key until after I install the game.

Any way out of this cursed loop?