Update: I have been unbanned!
As, I was not able to get in touch with OpenAI via the usual routes, I decided on the old school approach, and sent them a physical letter. I used an online service for this as I am not based in the US. While I never received a reply, my account has been reinstated and I do have access again, including all my old chats.
However, looking through the terms of OpenAI I stumbled across the disputes section. Up on reading this I also decided to open an dispute on the Online Dispute Resolution (ODR) platform of the European Union. The email address you can use is in the terms.
As I did both at the same time, I do not know what has lead to my unban, either the letter or dispute in ODR. However, it did eventually lead to an unban, so for everyone that wants their account back, there seems to be a way.