So, there is a thread with many pages of people who are unable to log in to Leviathan. The only place that works is housing districts. This was confirmed by someone in a housing area that did a search and found only 80 some people on the world - ALL in housing areas. Despite this, service call techs were insisting that the issue is due to players' network configuration and were told to contact their ISP.

7 hours later, SE have finally updated their issues notification to admit that there is a problem with Leviathan.

Seems there needs to be some "continuous improvement" done in the support department.