Customer management and invoicing

I am trying to make a website that doesn’t sell physical products or digital downloads. Customers contact us with their requirements, and we then invoice them. I want to be able to create a customer account, then have that customer log in and see their invoice, and be able to make either a full or partial payment with paypal or a credit card, with receipts being generated for each payment made. I would also like to be able to set a due date for the full invoice total to be paid by. So far I have tried using a few plug ins, but nothing seems to do what I need. so far the closest I have come across is wp-invoice, but this doesn’t tie an invoice to an account, it just provides a URL to view the invoice online and then pay with PayPal, but doesn’t offer card payments when using GBP as the currency.

is there a plugin that doesn’t require me to set up a shop, but just create invoices tied to a specific user account and have that user log in and pay with paypal or a credit card?