Okay, I found the answer after some more hunting. Apparently the only way to pull the standard posts is to add:
'operator' => 'NOT IN',
So it looks for posts that aren’t in the image post format. Or I have to add an array of terms to the terms line so it won’t return any of those formats. Odd, but it works.
<?php
$args = array(
'post__not_in' => $ids,
'showposts' => 10,
'cat' => '-4,-1866,-27',
'tax_query' => array(
array(
'taxonomy' => 'post_format',
'field' => 'slug',
'terms' => 'post-format-image',
'operator' => 'NOT IN'
)
)
);
query_posts( $args ); ?>
<!-- The Loop -->
<?php endwhile; ?>