Here is the code I ended up with that works. I should have mentioned that the query was inside the loop, because when I showed it to Damian Taggart of Mindshare Studios, he noticed that he said I should be using WP_Query instead of query_posts. Thanks to Milo and others for attempting to help me without having all the necessary info.
<?php
$paged = ( get_query_var('paged') ) ? get_query_var('paged') : 1;
$today = date('Y-m-d', strtotime('-6 hours'));
$myquery = new WP_Query(array(
'post_type' => 'exhibitions',
'posts_per_page' => 6,
'paged' => $paged,
'orderby' => 'title',
'order' => 'ASC',
'meta_query'=>array(
'relation'=>'AND',
array(
'key' => 'exstart-date',
'value' => $today,
'compare' => '<=',
'type' => 'CHAR'
),
array(
'key' => 'exend-date',
'value' => $today,
'compare' => '>=',
'type' => 'CHAR'
)
)
));
if ($myquery->have_posts()) :
while ($myquery->have_posts()) : $myquery->the_post();
?>