‘Sort by price’ filter not working with the default variation price

I have the following issue: almost all my products are variable products, which means that there is a price range. So in the beginning on the shop-page and homepage the price ranges where shown. But I wanted to display the default variation price I have set on the products. So I used to following code:

add_filter('woocommerce_variable_price_html', 'custom_variation_price', 10, 2);
function custom_variation_price( $price, $product ) {
    $available_variations = $product->get_available_variations();
    $selectedPrice = '';
    $dump = '';

    foreach ( $available_variations as $variation )
    {
        // $dump = $dump . '<pre>' . var_export($variation['attributes'], true) . '</pre>';

        $isDefVariation=false;
        foreach($product->get_default_attributes() as $key=>$val){
            // $dump = $dump . '<pre>' . var_export($key, true) . '</pre>';
            // $dump = $dump . '<pre>' . var_export($val, true) . '</pre>';
            if($variation['attributes']['attribute_'.$key]==$val){
                $isDefVariation=true;
            }   
        }
        if($isDefVariation){
            $price = $variation['display_price'];         
        }
    }
    $selectedPrice = wc_price($price);

//  $dump = $dump . '<pre>' . var_export($available_variations, true) . '</pre>';

    return $selectedPrice . $dump;
}

This code worked the way I wanted and right now on my shop all the products are displaying the default variation price. But the problem is now when I want to ‘sort by price’ from low to high or the other way around, it still on the price range. So when the price ranges are:

1.00 – 5.00 –> Default variation price is 2.50
1.50 – 6.00 –> Default variation price is 2.00
2.00 – 7.50 –> Default variation price is 2.25

It returns like this from high to low:

(1) 2.25
(2) 2.00
(3) 2.50

So my question is, what can I do to make sure that ‘sort by price’ sorts on the default variation prices which are shown to the customers.