Here's a followup:
Once more my sites are down and all access (HTTP, SSH) is blocked. They had it up for about 30 minutes earlier today.
An e-mail from tech support says that they think I am running Node (presumably NodeJS) because they detected calls to /modules/node/node.css in the server logs, and so they have banned my account.
Actually, that's a Drupal module that is the core of the entire Drupal system, nothing to do with NodeJS!
Meanwhile, another domain that is hosted on the same account still has the Phusion Passenger error that started when they screwed up the Passenger update two weeks ago. If I try to use PHPMyAdmin from the Dreamhost control panel, I also get the Passenger error.
All I need now is database access so that I can dump my databases. FTP is working (but not SFTP, because that relies on SSH), so I have downloaded all the assets and other important files. Once that is done, I have no reason to stay with Dreamhost and, given the experience of the past two weeks, I would be an idiot not to change.