UPDATE: I've managed to get everything working on Dreamhost without running PHP as CGI. (That is, everything WP-related that I use).
Dreamhost auto-CHMODs your domain to protect it when you turn off PHP as CGI. Initially, to test it really quick I changed the whole dern site to 777 (not recommended) just long enough to test the site, update permalinks and activate Text Control. It all worked. So, I re-CHMOD all the files to 644 and all the folders to 755. Exceptions are .htaccess, sitemap.xml and sitemap.xml.gz - which changed to 666. (Sitemap files for the Google Sitemap plugin). I got nervous about the .htaccess and changed it back to 644 after the permalinks updated.
General FYI, this info would have really helped me!