WooCommerce sidebar filter widgets not working with custom product WP_Query

Question

I am creating a custom template to display all products that have a positive stock value. I have also manually included the shop sidebar into my template as well using dynamic_sidebar. However the product attribute filter widgets in my sidebar aren't displaying, I assume because those widgets don't know how to 'talk' to my WP_Query to know what products are being returned and what attribute filters to even show. If I manually add the filter query string to the URL (for example - ?filter_color=gray) it's not filtering my WP_Query either, I assume because this is a WooCommerce query parameter, not a Wordpress / WP_Query thing.

So I guess my questions are, 1. is there a way to connect my WP_Query to WooCommerce's attribute filter sidebar widgets, and or is there a better way to build out a custom template that's showing only products with positive stock values that's also filterable using WooCommerce's attribute filter widgets?

My WP_Query:

<?php
    $args = array(
        'post_type' => 'product',
        'posts_per_page' => 1000,
        'meta_query' => array(
        array(
            'key' => '_stock',
            'value' => '1',
            'compare' => '>',
        )
    ),
    'meta_key'          => '_stock',
        'orderby'           => 'meta_value_num',
        'order'             => 'DESC'
    );
    $loop = new WP_Query( $args );
    if ( $loop->have_posts() ) {
        while ( $loop->have_posts() ) : $loop->the_post();
            wc_get_template_part( 'content', 'product' );
        endwhile;
    } else {
        echo __( 'No products found' );
    }
    wp_reset_postdata();
?>

My sidebar code:

<?php dynamic_sidebar( 'shop-sidebar' ); ?>