I once visited a forum which let you download either all or selected private messages to a single text file, which was convenient for saving a local copy of messages before I deleted them. Does this forum have anything like that?

Click 'Archive messages' in 'My Controls', that will have your messages e-mailed to you in a single file.

You can go to your message inbox and click the link saying Archive Messages on the left in the menu.

It should take you to this.