set_price() not working in nested foreach

I am trying to set the price of a product to 0 in a nested foreach loop. Maybe I am thinking about the whole problem wrong, but I can’t get it to work. If I do $cart_item['data']->set_price('0'); at the top of the first foreach, it works (and sets the price to 0 for all products).

But when doing it inside the last foreach, near the bottom of the code block below, nothing happens. The price is not visually set in the cart. I have checked the cart item object, and the changes:protected part of it is updated with the new price of 0.

I have also checked that I actually reach that line of code. What I want is to set the price of the split item to 0, but not the other items that are not split.

What am I doing wrong?

        if (is_admin() && !wp_doing_ajax()) {
            return;
        }

        if (did_action('woocommerce_before_calculate_totals') > 1) {
            return;
        }

        $compatible = false;
        $thecart = $cart->get_cart();

        //Check if we have any compatible items
        foreach ($thecart as $cart_item) {

            $postid = $cart_item['product_id'];
            $quantity = $cart_item['quantity'];

            //Check if the item is a 3for2 item
            if (!$this->get_3for2_status($postid)) {
                //Not a 3for2 item
                continue;
            }

            //If yes, check if the amount added is compatible with the 3 for 2 discount
            if ($quantity < 3) {
                //Not compatible with discount
                continue;
            }

            //Set compatible flag to true
            $compatible = true;
        }

        //Don't continue if we have no compatible products
        if ($compatible != true) {
            return;
        }

        //Get number of items to be free

        $quantity = 0;

        foreach ($thecart as $cart_item) {

            //Check if the item is a 3for2 item
            if (!$this->get_3for2_status($postid)) {
                //Not a 3for2 item
                continue;
            }

            $quantity += $cart_item['quantity'];
        }

        $freequantity = intdiv($quantity, 3);

        //Loop the cart to split free items from the cheapest item
        //Do this while we still have free items to give

        while ($freequantity > 0) {

            $pricearray = [];

            foreach ($thecart as $cart_item) {
                $id = $cart_item['product_id'];
                $price = $cart_item['data']->get_price();

                //Don't add free products
                if ($price > 0) {
                    $pricearray[$id] = $price;
                }
            }

            //Split the lowest priced item into a free one
            $splititem = array_search(min($pricearray), $pricearray);

            foreach ($thecart as $cart_item_key => $cart_item) {
                $id = $cart_item['product_id'];

                //Only check the lowest priced item
                if ($id != $splititem) {
                    continue;
                }

                $quantity = $cart_item['quantity'];

                //If there is only one left, set price ... 
                if ($quantity == 1) {
                    $cart_item['data']->set_price('0');
                    continue;
                }

                //... otherwise, split item

                //Set quantity to quantity - 1 for the item
                $cart->set_quantity($cart_item_key,  $quantity - 1);

                //Then split 1 of the item

                //Set a unique key.
                $cart_item['unique_key'] = uniqid();

                //Store the unique key
                $uniqkey = $cart_item['unique_key'];

                //Get variation vars
                $variation_id = $cart_item['variation_id'];
                $variation = $cart_item['variation'];

                //Add the product as a new line item with the same variations that were passed
                $cart->add_to_cart($id, 1, $variation_id, $variation, $cart_item);

                //Do a new fetch of the cart and loop it again
                foreach ($cart->get_cart() as $cart_item) {

                    //Check that we handle the correct item
                    if ($cart_item['unique_key'] != $uniqkey) {
                        continue;
                    }

                    //Set the price to be free
                    $cart_item['data']->set_price('0');
                }
            }

            $freequantity -= 1;
        }