Hi,
For the complaints about render blocking js and css, you could consider enabling defer_javascript and prioritize_critical_css to see how that works out.
(The docs also describe risks associated to enabling these filters)
Some of the images in the first site you mentioned are injected via javascript. As mod_pagespeed does not interpret javascript, these images can only be optimized in-place, without changing the urls that reference them). That means that some optimizations cannot be applied to them.
One thing that may help here is enabling browser-specific in-place optimization:
It may also be worth it to take a look at what the debug filter logs in html comments (one way to enable it is by adding ?PageSpeedFilters=+debug to the querystring of a page) to see if there are any useful messages written in html comments.
Otto