Is there any standardized technique for assured data deletion in the cloud?
For some definition of standardized, yes: store data encrypted (symmetrically or with hybrid encryption) in the cloud, with decryption by the legitimate user in an environment they trust. Destruction of the data is by destroying the decryption key, and requiring the cloud storage provider to stop billing for the storage. It's then their best interest to destroy the ciphertext, and we do not care if they act otherwise. We are back to a (difficult) problem of key management, with the volume of the data immaterial.
A common name for that is Client-Side Encryption Cloud Storage.
Many of the other solutions I read about are insecure, or/and detached from reality and standard common sense assumptions. E.g. this article admits
it is difficult for the cloud server to return a technical proof by which the data owner is convinced that their data are deleted
and instead proposes that
after the deletion of the data, the cloud server can return a message (“Delete, fname”) and its signature Sig(“Delete, fname”), where fname denotes the file name of the deleted file. The signature can be viewed as a publicly verifiable evidence which indicates that the file has been deleted successfully.
That's undeniably a cryptography-based solution, but it's security rests on the assumptions that the cloud server provider is trustworthy, and that no copy was made of the data, by that provider or otherwise.
The risk of data copy is brushed away by that same article when it discusses storing a file in the cloud, allowing access to multiple users, and then hoping for secure deletion. As long as at least some fraction of users have a computer they control (which I hope is for long), this won't be.