Leslie,
We have a similar system. Here is what we do. We enter the payment into the PM program using the EOB date. EOBs are each scanned to Paperport into a folder for the year with subfolders labeled by insurer: Medicare, Carefirst, Commercial; each scanned EOB is titled with its date.
Then, if we need an EOB for a specific billing for a patient, we check the payment entry date in the PM program, and can pull up that EOB easily in Paperport. It can then be reviewed or printed as needed.
This obviously does not separate them by patient, but it works well for us.