How can I cache pages indefinitely?
The setting on the performance page, unlike D6/7, does not affect the page cache module at all. The page_cache module always caches indefinitely, you can not configure it otherwise. Invalidation happens through cache tags, as you said.

The setting that you can see only affects external caching through the HTTP Cache-Control header, for example Varnish and in browsers. There are ways to invalidate caches in varnish using cache tags, but there is none to invalidate pages that are cached client-side in browsers, so I would recommend to not set that value too high.