As an employee, I was overpaid one Christmas. I didn't notice because at that time, we did earn more thru overtime, so I just accpted it.
They had the right to claw the money back, which they did. However, originally they wanted to do it in one lump, which would have meant me working a week for nothing. In the end, a part payment by installments was negotiated.
The thing is, you made a mistake with payments which you are entitled to get back one way or another. As I see it, you can do what you suggested, or you can collect what is due next pay day, either in whole or a part. If it really isn't a lot for the individual, and if you are as good as you say, they cannot really object - they don't have any rights to the overpayment anyway.