Assume you're Satoshi Nakamoto, completely, and that you've forgotten your private key/s. How do you prove that this is true, using the BTC blockchain? Is there a transaction you can make, or a message you can sign? Remember, you don't remember your private keys.
...you've forgotten your private key/s. How do you prove that this is true
You cannot prove that you have forgotten something. How would you prove you don't have a secret backup hidden away?
Is there a transaction you can make, or a message you can sign?
No, making transactions and signing messages are both actions that require the use of your private key to complete.
Satoshi Nakamoto posted often on BitcoinTalk. If he would be able to log in and post a message revealing his true identity, it would likely be convincing.