Must have read this post about five times before I understood what was going on: http://wordpress.org/support/topic/plugin-gigs-calendar-shortcodes-php-templates-commands-documentation-please?replies=6
So I thought I would share the temporary answer to my question.
I disabled the display of my 30+ archives by setting
Gigs Calendar > Settings > Select a page to house your gigs archive: to --None--
Then I displayed the latest 20 entries of the gigs archive by adding the code below to the page where i wanted the gigs archive to show up:
[gigs-cal archive limit=20]
Done! Pretty sweet, though I'd like to find a way to view the entire gigs archive eventually, 20 entries at a time...
Also, how in the world does gigs-list.php know to loop through if you want to display both upcoming and past shows archive? Is it in this piece of code on gigs-list.php (wp-content/gigs-templates/my-own-template folder),
<table class="gigs calendar <?php $upcoming ? 'upcoming' : 'archive' ?>">
or is it in gigs-calendar.php (wp-content/plugins/gigs-calendar folder)? Sorry if the answer to this question is super obvious.