The unapplied payment I'm referring to is our customer’s overpayment (showing in A/R reports).

I have been scratching my head on this problem, and even asked google's gemini ai for solutions; it gave a l-o-n-g solution, that I hope is not necessary, but it did provoke some additional thoughts for me, since the received payment increases "income"....

I think I have a simple, clean solution; but I would really appreciate some feedback to make sure I'm not overlooking something.  Will this work: 

1. create a new item named "AR Payment Adjustment" (type = service) linked to existing contra-income account, "Sales Returns & Allowances".

2. create an invoice to this customer for this item "AR Payment Adjustment"

3. Apply the erroneous payment to this new invoice

Any problem with this method?