how to fire theme preprocess hooks for specific panes that don't already exist

In at_pe, one of the available panes is Page navigation, which is handled in template.php by at_panels_everywhere_preprocess_pane_navigation. This is great, but for my current project I need to split page navigation into two different columns, which means that I'm instead using page primary links and page secondary links instead. While I've managed to override the output for secondary links by providing a panels-pane--page-secondary-links.tpl.php template file, I can't seem to find the appropriate hook to call to preprocess data sent to that template.

So what I need to find out is either:
how the pane-navigation.tpl.php file is called and how it knows to call the correct preprocess function, so that I can make my own versions (pane-primary-navigation / at_panels_everywhere_preprocess_pane_primary_navigation() )
or
how to appropriately hook into the page generation process (what would normally be x_preprocess_page, but not that since it doesn't get called for PE themes) so that I can perform the necessary preprocessing on the primary and secondary navigation structures.

I feel like I'm missing something really obvious here - it seems to clear in the pane navigation template and preprocess theme, but I've been unable to replicate the way that works, so I have to assume that pane_navigation is special in some way, or that I need to name it somewhere as a special template with corresponding preprocess hooks so that the variant that I want to create for secondary links actually fires.

And just in case I'm asking entirely the wrong questions through inexperience, what I'm actually trying to accomplish here is to render three different menus in three different columns, where the third menu is actually the expanded menu tree and not just the top level links:
menu_1 / main_menu / another_menu (as a tree)

Thanks! And sorry if this question is obvious and/or covered somewhere else.