I think I'd make a similar recommendation to my comments on this post at Drupal.org. Basically, if you create a product called "invoice payment" or something similar with an attribute called invoice # and no options, you should be able to use the cart links module to create a button on someone's invoice that will add the payment product to the cart w/ the correct invoice # and send them to checkout. You'll need a custom module to load up the invoice using hook_cart_item() and the invoice # you specify and adjust the price of the item accordingly. I'd say it's maybe a couple hours' work to get a going.

If you're loading that price based on some value for that product (like an invoice number) with the hook I mentioned, then it will be a per instance price. You'll need to do some authentication on it, but I don't foresee any trouble with it.