How can I permanently cache or “archive” a WP blog without needing future maintenance

I think HTML mirror is the way to go here.

There is no point keeping dynamic site that doesn’t need to be. And leaving it unmaintained is not really possible on auto-pilot – even if updates are automatic there is no guarantee some plugin won’t get just dropped by developer.

Alternatively you can build multi-design site. It’s not that hard to load stylesheets and templates conditionally. Of course that would be considerable amount of work comparing to HTML mirror.