Update: Tried again at 2PM Monday, and it worked, twice. Noticed unusual behavior:
When ME3 is working properly, the 'connecting to EA' message doesn't appear until the menu screen -- and then the menu opens and the checking DLC message appears, twice.
When ME3 is _not_ working, the 'connecting to EA' message appears on the title screen -- and then the 'checking DLC' message appears on the menu screen twice, before the menu appears and the 'unable to authorize...' message appears. Does this help indicate what was going wrong?