Thank you so much for all of this information to help clarify what you’re needing.
Based on what you’re saying the option that would work best for you is to use the Draft Order feature and split the payments up that way. I know it isn’t as intuitive as you’d like, but it will cut out the steps of using square and copying the information over.
If you have your customer’s contact information you can send them an invoice directly from the draft order so that they can pay there, the money is tracked and inventory is adjusted appropriately. The invoice won’t have any information from the previous payment invoice, but you can add that information in the notes.
From the options available in association with what you need I think this would be the best option for you.