This isn't something PageSpeed really offers right now.
> landing page for new visitors, who are identified by the lack of a cookie
> or if they land on some predefined URL (mostly inlining stuff)
For this you could set up
https://developers.google.com/speed/pagespeed/module/downstream-caching
and use a cache between PageSpeed and the user instead of optimizing a
static site.
> email newsletter (mostly HTML cleanup)
HTML email is pretty different from HTML for browsers. A tool that's
specialized for email would probably do a much better job and be less
likely to include things that some email clients would reject. These
email-specific tools are also helpful with automating the kind of
inlining you need to do with your css for HTML emails.
Jeff