Perhaps you could use a 'composite table' that combines the AR customer master and the current transactions tables into a single view. Then you can use a filter that searches for the customer outstanding balance = 0 AND transaction current balance <> 0. This should list all transactions (invoices and cash) for the zero-balance customers.

If you use the 'Write-off batch' function in AR and only choose to write off Balances of a range from zero to zero, this will create an adjustment batch that will select all of the same transactions that the GridView view above would select.