Nevermind.
In case anyone is interested, here’s what I did to solve this for myself:
In wp-content/themes/[theme in use]/index.php, the following line is what causes the date to appear below the heading for each individual post:
<small><?php the_time('F j, Y') ?> <!-- by <?php the_author() ?> --></small>
I copied that and pasted it into wp-includes/widgets.php after this (somewhere around line 908, according to my HTML editor):
<li><a href="<?php the_permalink() ?>"><?php if ( get_the_title() ) the_title(); else the_ID(); ?> </a>
I also added a linebreak so that the date appears beneath its respective article heading in the “Recent Posts” block. So, altogether, this is the line that now appears in wp-includes/widgets.php:
<li><a href="<?php the_permalink() ?>"><?php if ( get_the_title() ) the_title(); else the_ID(); ?> </a><small><?php the_time('F j, Y') ?> <!-- by <?php the_author() ?> --></small></li>