library journal

Very briefly, to help with suggestions of library world publications with more of a lefty perspective:

Counterpoise often reviews lefty publications regularly. I know that they depend on volunteer reviewers to provide content (I am not sure how this might compare to the other library publications you mention above).
For more info: www.counterpoise.info

You may also want to look into the Alternative Press Index:
"The Alternative Press Index (API) was born with the New Left of the 1960's. It was launched in 1969 to provide access to the practices and theories of radical social change. The Index is international and interdisciplinary, spanning the social sciences and humanities, with its central focus on the practice and theory of socialism, national liberation, labor, indigenous peoples, gays/lesbians, feminism, ecology, democracy, and anarchism. It strives to be as comprehensive as possible."

API indexes and annotates more serial (magazine or newspaper) articles, but includes a wide variety of small press titles.
Their website: www.altpress.org/mod/pages/display/8/index.php?menu=

I am not sure how either of these would play into requirements for librarians to have materials (positively) reviewed before they can be added to library collections. I am eager to hear what information others may have on this topic.