Have you found a solution for this?
Draft Order shouldn't requires that much manual work. While switching the whole POS system would be a complicated process, I still want to recommend a POS system that allows you to create Draft Order and save it for later checkout. It's ConnectPOS.
Besides the basic POS features, you can add items to cart, and save the cart for later checkout. The draft order is then listed within the POS and can be retrieved easily.
My only question is: Do you need to allow customers to partially pay for the draft order?
I'd be happy to add you to the list but I need your store URL to do that.