The church secretary should be able to install and use the CMS on almost any shared hosting account.

My translation: must be written in PHP or else be fully client side, not need any configuration, and come with an FTP HOWTO for people who barely know that e-mail uses the same network as "internet" (the web).

The templates should not make your staff page and copyright page look just like another blog entry.

My translation: it must not be blogging software, but a generic CMS.

Content management is useless if you have to recreate your website to use it. Your CMS should be able to manage your current website as-is.

My translation: no templates, but direct application on existing, unmanaged pages. Consistency is established by copying empty pages and never changing anything in the base design.

Tabbed, paged, treed, etc. control panels do not make your CMS user-friendly. They make it overly complicated, and they are not very sexy.

My translation: there must be no features in the system and it may not be suitable for large websites. Structured content doesn't work, and the target site has no more than 25 pages.

Content deserves to roam free instead of being trapped in complex databases.

My translation: I want an editor to work with raw HTML pages.

I'm sure you will find the CMS you're looking for. Any Wysiwyg editor with built in FTP client suffices. But you will not find one that corresponds entirely to all of your demands, simply because then it does suck, and one of your demands is that it doesn't. Tricky.

Good luck.