@Confuzzo
It sounds like EAC is using the C drive as its directory for certain files, which may just be hard coded into the program. I don't know if we have a way of forcing it not to save those files there.
There is something else I was curious about. Have you tried installing BF2042 through the EA App instead of Origin? I've seen a few people mention they were able to get the game running that way.
You can find more info on the EA App over at the EA Help website. If you're able to give it a try please let me know how it goes. Thanks!