Hi Anna,
I see your point,
Have you tried on the option that you create long term PO and create down payment against it, with deliveries you can create Inbound Delivery everytime you want to post goods receipt as notification/confirmation in PO and post goods receipt against IBD rather than PO.
This way you have full tracking of all deliveries and can settle downpayment against PO as you like.
One way of doing it whilst fulfilling all requirements.
Khurram