Nevermind -- FINALLY got through. First, you have to ignore the "press 1 if you're a customer, press 2 to activate a card" initial prompt -- twice.
Then, at "Press 1 or say 'lost or stolen' to report a lost or stolen card," DO NOT PRESS 1 -- say "lost or stolen."
If you press 1, you'll be asked to "press 1 to report a lost or stolen card," without an oral option, but it won't recognize you pressing 1 and will hang up on you.
If you go with oral options, you can get through to a real person.
TERRIBLE phone system. Terrible.