Custom Post Pagination Not Working - php

Question

I know there have been so many pagination questions, but I'm really stumped here. I have a "gallery" hierarchical custom post type. For the parent posts, I'm using an index template, and the child posts uses more typical single page code.
Here's some of the single-gallery.php file. I just check to see if the post has children. If it does, I want it to be an index page.
get_header();
$template = get_template_directory_uri();
//If it's an index page, redirect it
$args = array(
'post_parent' => $post->ID,
'post_type' => 'gallery',
'numberposts' => -1,
'post_status' => 'publish'
);
$children = get_children( $args );
if ($children){
get_template_part('template-parts/content', 'gallery-index');
get_footer();
} else{
After that else, it outputs all the code for the single display, which is working fine.
In content-gallery-index.php, I have.
$paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1;
Then it goes on to handle code for another, unrelated page. Lower in the template, I have the following (I included all of it by request):
<?php elseif (is_page(343) || $post_type == 'gallery' ):
$post_parent = 343;
$type = 'page';
if ($post_type == 'gallery'){
$post_parent = $post->ID;
$type = 'gallery';
}
$args = array(
'post_type' => $type,
'post_parent' => $post_parent,
'posts_per_page' => 6,
'paged' => $paged,
);
$query = new WP_Query($args);
if ($query->have_posts()): ?>
<div class="box-steps">
<?php while($query->have_posts()): $query->the_post();
$image = get_the_post_thumbnail();
$permalink = get_the_permalink();
if (!get_field('dont_include_in_services')): ?>
<section class="box-step">
<div class="box-step-img-wrapper">
<a href="<?php echo $permalink; ?>">
<?php the_post_thumbnail(); ?>
</a>
</div>
<div class="box-step-content-wrapper">
<h2 class="box-step-title our-services-title header-font"><?php echo get_the_title(); ?></h2>
<?php if ($post_type == 'gallery'): ?>
<p class="box-step-content"><?php echo get_the_content($post->ID); ?></p>
<?php else: ?>
<p class="box-step-content"><?php echo esc_html(get_field('preview_text')); ?></p>
<a class="box-step-link block bold" href="<?php echo $permalink; ?>">
READ MORE
</a>
<?php endif; ?>
</div>
</section>
<?php endif; ?>
<?php endwhile; ?>
</div>
<?php endif; wp_reset_postdata(); ?>
<!-- pagination here -->
<?php
custom_pagination($query->max_num_pages,"",$paged);
?>
<?php endif; ?>
functions.php
function custom_pagination($numpages = '', $pagerange = '', $paged='') {
if (empty($pagerange)) {
$pagerange = 2;
}
global $paged;
if (empty($paged)) {
$paged = 1;
}
if ($numpages == '') {
global $wp_query;
$numpages = $wp_query->max_num_pages;
if(!$numpages) {
$numpages = 1;
}
}
$prev_arrow = is_rtl() ? '»' : '«';
$next_arrow = is_rtl() ? '«' : '»';
$pagination_args = array(
'base' => get_pagenum_link(1) . '%_%',
'format' => 'page/%#%',
'total' => $numpages,
'current' => $paged,
'show_all' => False,
'end_size' => 1,
'mid_size' => $pagerange,
'prev_next' => True,
'prev_text' => __('«'),
'next_text' => __('»'),
'type' => 'list',
'add_args' => false,
'add_fragment' => '',
'prev_text' => $prev_arrow,
'next_text' => $next_arrow,
);
$paginate_links = paginate_links($pagination_args);
if ($paginate_links) {
echo "<nav class='custom-pagination'>";
//echo "<span class='page-numbers page-num'>Page " . $paged . " of " . $numpages . "</span> ";
echo $paginate_links;
echo "</nav>";
}
}
The strange thing is that the numbered pagination is output fine, but when I click on page two, it's like the URL just gets rewritten and the page just refreshes. This same code has worked on another page, but that page is not a custom post type. I've also tried the trick of turning wp_query to null and resetting it, but then I get other errors.