Ok, possible solution for K2. First, you need to edit K2's theloop.php template. In there, locate this section:
<?php
/* Check if there are posts */
if ( have_posts() ) {
You want to modify this php tag by slipping in the following just after <?php but before the /* Check if there are posts */ line:
if ( is_home() && !$_SERVER['QUERY_STRING'] ) {
$latest = $wpdb->get_var("SELECT post_date FROM $wpdb->posts WHERE post_status = 'publish' AND post_type = 'post' ORDER BY post_date DESC LIMIT 1");
$latest = str_replace('-', '', substr($latest, 0, 10));
query_posts('m=' . $latest . '&showposts=-1');
$wp_query->is_archive = false; $wp_query->is_home = true;
}
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EDIT: Stuck in the $_SERVER[] portion of the if test to deal with that steekin' archive link/scrollbar. Not perfect though ('older' posts rely on standard query/posts_per_page, so it can be off from the home page).