've got a similar idea that might share a solution: a custom payment link.
We currently accept payments through Ubercart on our web site. I've set
up an invoice product there, with fields for amount and invoice number.
I can construct a link that adds the product to the user's cart with
appropriate values and takes them straight to checkout.
I'm sure you can do the same with Paypal -- construct a payment link.
What would be highly useful is to have some sort of link builder
available in LSMB, to auto-generate a payment link using rules specified
by an admin... I see wanting to do this from both individual invoices as
well as AR -> Aging.