Well – this is finally fixed, with the help of my hosting company (www.isomedia.com). The issue was that “Magic Quotes” were enabled on my server’s default PHP settings. Seems like WordPress ought to deal with this stuff automatically, regardless of random server defaults – oh well, I guess not.
The specific solution was to add some lines to the .htaccess file in the /wordpress directory:
php_flag magic_quotes_gpc off
php_flag magic_quotes_runtime off
