Magento – Can’t set shipping method on order created programmatically

I have been searching for an answer on the web, but have tried all the solutions I have found and nothing seems to work.

The order adds fine, but in the admin panel is shows "No shipping information available".

When I go through the cart, then it shows "Free Shipping".

Any ideas on how to set the shipping method on the order?

           //Product to add to the order
           $product = Mage::getSingleton('catalog/product')->load($productId);

            //Previous order to copy from 
            $order = Mage::getModel('sales/order')->loadByIncrementId($orderId);
            $converter = Mage::getModel('sales/convert_order');
            $quote = $converter->toQuote($order);

            $quote->setBillingAddress($converter->addressToQuoteAddress($order->getBillingAddress())); 
            $quote->setShippingAddress($converter->addressToQuoteAddress($order->getShippingAddress()));
            $quote->getShippingAddress()->setShippingMethod("tablerate_bestway"); 
            $shippingAddress = $quote->getShippingAddress();
            $shippingAddress->setFreeShipping( true )
            ->setCollectShippingRates(true)->collectShippingRates()
            ->setShippingMethod(‘tablerate_bestway’)
            ->setPaymentMethod(‘checkmo’);

            $quote->setStore($order->getStore()); 
            $quote->setCustomer($customer);
            $converter->paymentToQuotePayment($order->getPayment(), $quote->getPayment()); 




            $convert = Mage::getModel('sales/convert_quote');


            $newOrder = Mage::getModel('sales/order');

            $payment = $convert->paymentToOrderPayment($quote->getPayment());

            $newOrder->setPayment($payment);
            $newOrder->setBillingAddress($convert->addressToOrderAddress($quote->getBillingAddress())); 
            $newOrder->setShippingAddress($convert->addressToOrderAddress($quote->getShippingAddress()))->setShipping_Method('tablerate_bestway'); 
            $newOrder->getShippingAddress()->setFreeShipping(true);
            $newOrder->setShippingMethod('tablerate_bestway');
            $newOrder->setCustomerId($customer->getId()); 
            $newOrder->setCustomerFirstname($customer->getFirstname());
            $newOrder->setCustomerLastname($customer->getLastname()); 
            $newOrder->setCustomerEmail($customer->getEmail()); 

            $newOrder->setState(Mage_Sales_Model_Order::STATE_PROCESSING,true);
            $order->setWeight($product->getWeight());

            $newOrder->setSubtotal($product->getPrice())
            ->setBaseSubtotal($product->getPrice())
            ->setGrandTotal($product->getPrice())
            ->setBaseGrandTotal($product->getPrice());


            $message = 'Generated Order';
            $newOrder->addStatusToHistory($newOrder->getStatus(), $message);

             $orderItem = Mage::getModel('sales/order_item')
            ->setStoreId($newOrder->getStore()->getStoreId())
            ->setQuoteItemId(NULL)
            ->setQuoteParentItemId(NULL)
            ->setProductId($product->getId())
            ->setProductType($product->getTypeId())
            ->setQtyBackordered(NULL)
            ->setTotalQtyOrdered(1)
            ->setQtyOrdered(1)
            ->setWeight($product->getWeight())
            ->setIsVirtual(0)
            ->setIsQtyDecimal(0)
            ->setQtyInvoiced(1) 
            ->setName($product->getName()." Generated")
            ->setSku($product->getSku())
            ->setPrice($product->getPrice())
            ->setBasePrice($product->getPrice())
            ->setBaseOriginalPrice($product->getPrice())                
            ->setOriginalPrice($product->getPrice())
            ->setRowTotal($product->getPrice())
            ->setBaseRowTotal($product->getPrice())
            ->setOrder($newOrder)
            ->setProductOptions($savedOptions);

            $newOrder->addItem($orderItem);

            $newOrder->save();

            $invoice = Mage::getModel('sales/service_order', $newOrder)->prepareInvoice();
            $invoice->setRequestedCaptureCase(Mage_Sales_Model_Order_Invoice::STATE_PAID);
            $invoice->register();
            $invoice->setAmount($grandtotal);
            $invoice->pay()->save();
            $transactionSave = Mage::getModel('core/resource_transaction')
            ->addObject($invoice)
            ->addObject($newOrder);

            $newOrder->save(); 
            $transactionSave->save();

            $payment->pay($invoice);