"Sorry, it appears the EA Servers are currently down. We are working to address

I have a fix for the SP version not authorizing DLC.

Log into the social.bioware.com site, keep that window open.
Log into Origin.
Right click ME3 and select repair.
Wait a ridiculous amount of time for it to check every single file (mine was 17 files).
Once it's done repairing, launch the game (with the social window still OPEN)

Worked for me. GOOD LUCK!