ChatGPT provides a new Apps SDK that makes things easier. The MCP server does need a proper Authorization Server to do OAuth, including DCR and OIDC metadata support, but those are the best way to do what they are trying to do. Anything else I have considered would be much worse security and discovery wise.
So far, I was not able to do it. And there are no examples that I can find. It's also all complicated by the total lack of logs from ChatGPT detailing the errors.
I'll probably get there eventually and publish a blog...