Hi,
1. AR down payment invoice is closed when you raising incoming payment. So this AR down payment invoice will not appear in incoming payment selection list
2. Further due to partial payment, only AR invoice will be in open status and this AR invoice will appear in incoming payment selection
3. If you want use Payment on account for balance amount, are you able to choose customer account at GL account field?
4. I don't think it is possible to post balance amount via payment on account. To get correct BP account balance, we have to post at customer account.
Let me know your feedback.
Thanks & Regards,
Nagarajan