I agree that this should be the first focus. Most of us will be getting the digital version of the game, and EA's Origin application will be how it is delivered. I am certainly not happy to see another Steam-type plague upon the world, but it is what it is.
The Origin client application is freely downloadable from EA (after creating a free account), and it currently does not work with Crossover Games. It installs and runs the first few screens, but when it gets to what I assume is the main content screen I see only a black box with some artsy corners, and it hangs hard there. I must kill it via the Manage Bottles interface, but even then it often stays on screen, atop other windows. This sequence is repeatable.
I would certainly be willing to help test this out, but I have no experience with debugging within Crossover products. I read well and learn fast, though, so if any devs would like to point me in the right direction I'll get started.