How to correct project information on a PO , after a payment is already made against an incorrect pr

My Purchasing user selected an incorrect project and task when creating the purchase requisition (which went on to the PO, and eventually on to AP). Payment has been issued against that project and task.

After realizing that the original entry was incorrect, the Purchasing user wants to correct the project and task information on the PO. How can we accomplish this in the best possible manner?

One thought that came to my mind is that we can do a RTV transaction, which would create debit memo after which I can go to the PO Distribution and cancel the original PO distribution. That should relieve the incorrectly charge task and project. After that, I can add the correct project information on the PO distribution, and recreate new invoices and a payment against that.