Good to hear from you again. Thanks for your question and for including the full source text of your shortcodes; very helpful.
Your goal is similar to that described in the “An example of the paginate_links output type” section in the Settings/Media Library Assistant Documentation tab. The detail you’re missing is that you need two separate shortcodes, one for the pagination controls and one for the gallery display. They must have identical data selection parameters so the items retrieved by each shortcode are the same.
Here are two shortcodes that should work for your application:
[mla_gallery attachment_category=id-articles orderby="date DESC" posts_per_page=40 post_mime_type=application/pdf mla_output="paginate_links,prev_next" ] [/mla_gallery]
[mla_gallery attachment_category=id-articles orderby="date DESC" posts_per_page=40 post_mime_type=application/pdf columns=5 mla_viewer=true size=full link=file mla_target=_blank] mla_caption='<h3><a href="https://projectdmc.org/support/topic/paginate-pdf-galler/{+file_url+}" target="_blank">{+title+}</a></h3><h6><b>Species Mentioned: </b>{+terms:attachment_tag+}</h6><h6><b>Date: </b>{+date,date(Y-m-d)+}</h6>' [/mla_gallery]
I removed the post_parent=all because the attachment_category= parameter sets it automatically. I retained the [/mla_gallery] in the first shortcode because WordPress will combine the two shortcodes into one (corrupted) shortcode without it.
I am marking this topic resolved, but please update it if you have problems or further questions regarding the suggested solution. Thanks for your continued interest in the plugin.