Split payment with backorders

We have a shop that allows backorders when a product is not in stock. What we want to do is when a customer placed an order, split that order based on products that are in stock and can be shipped instantly and products that are not in stock and are in backorder. Those split orders need to have the same order number or the original order number with a suffix so customers can see that it is part of the original order.
Second problem is that we only want to charge the customer for the products that are actually leaving out warehouse. So one invoice for all the products that are in stock and will be shipped instant, and one invoice when the backordered products are back in stock and will be shipped.
Does somebody have any idea how to get this done. We already searched for different plugins or custom code solutions (like split order plugins and pre-order plugins) but they never do what we want like descriped above.