@Rainflurry 

The app used the same Name for both the debits and the credits to Accounts Receivable for all transactions.  The journal entries net to zero (under that customer's name in the Open Invoices report).

The very first thing we did was go to Customers/Receive Payments and select that name.  However, there are hundreds and hundreds of lines.  We have only been able to do the cleanup line-by-line.  We have not been able to apply the credits in one fell swoop. 

If you test it out by making the journal entries that the app made (earlier post) - and make a bunch of them - I think you will find you have to select each line, apply a credit, then select the next line, apply a credit, etc.

I could do it if they were in Enterprise or if I still had my Accountant's copy of Premier because with that I would have Accounting Tools/Fix Unapplied Customer Payments and Credits.  That works in bulk, or in one fell swoop, as you say.  They are in Pro (NOT an Accountant's version) so they don't have "Fix Unapplied Customer Payments and Credits."  I can't restore their data to Enterprise to do it.

And by the way, Intuit's customer support (both on the phone and above) did not know about Accounting Tools/Fix Unapplied Customer Payments and Credits - the One Fell Swoop solution.