The Parliamentary Ombudsman (PO) can carry out independent investigations into complaints about government departments. You will be complaining about HMRC, and possibly even the Adjudicators Office and their handling of your complaint / dispute.
The PO investigate that the service being complained about kept to its own policies. In this case that is HMRC's COP26. And so to take your case to the PO it really needs to be due to feeling that COP26 has still not been applied correctly.
Cases must be referred to the PO via your MP. Note that your MP cannot refuse to refer your case to the Parliamentary Ombudsman and you do need the MP to be the one to send the initial complaint in. So see this page for how to contact your MP if you haven't already. I would send a copy of your previous letters to the AO and a simple cover letter to your MP asking them to refer your complaint and dispute to the Parliamentary Ombudsman.
Again, it is possible to receive a partial success at this stage. The PO may decide that HMRC are responsible for one or more portions of the overpayment and rule that this portion be written off, or HMRC may even admit to it in their response to the PO.
This stage is only over if and when the Parliamentary Ombudsman writes to inform you they have “decided not to uphold part or all of your complaint”. If you do not accept the PO's decision, it is possible to respond in writing to the PO complaining of any issues you feel have not been considered fully, or that you feel the decision is unreasonable. Although, if these particular issues have already been addressed by the Parliamentary Ombudsman, they are unlikely to change their stance.
If you experience demands from HMRC to repay during disputing please see our page about Harassment.
Still not got a fair outcome? Then it's time to take a look at your final possibilities in Dispute Step 6.