Is it possible to create 2 unique titles for an Events custom post type: Upcoming Events and Past Events?

Try this: in archive-header.php line 8 – 10 by interecepting the variable “period=past” or ( I guess) “period = future” of current URL

<?php else :
  if( !empty($_GET['period'] ) && $_GET['period'] == 'past')
  {
    echo "Past Events";
  }
  elseif( !empty($_GET['period'] ) && $_GET['period'] == 'future' /*or whatever*/){
    echo "Upcoming Events";        
  }
  else{
    echo esc_html(lsvr_pressville_get_event_archive_title());//the default output of your theme function
  }

  endif; ?>