I SOLVED IT!
The problem is that I am using NextGEN Basic Thumbnail, so even though my template is custom, it is a LEGACY template.
I yanked the following bit of code from here:
https://hookr.io/functions/nggv_gallery_vote_form/
<?php
if(isset($gallery->displayed_gallery) && isset($gallery->displayed_gallery->container_ids)) {
if(count($gallery->displayed_gallery->container_ids) == 1 && is_numeric($gallery->displayed_gallery->container_ids[0])) {
$gid = $gallery->displayed_gallery->container_ids[0];
}
}
?>
Then put $gid into the Custom Fields tag replacing the $gallery->ID, like so:
<?php echo nggcf_get_gallery_field($gid, "Your Gallery Field Name"); ?>
Ba Boom!