Is it permissible to say: "O Allah, to You be all praise, the praise of the the thankful, and the gratitude of the praisers," and is there any evidence for it from the Qur'an and Sunnah?

This supplication is not mentioned in the books of Sunnah. It is better to praise Allah using the established formulations. Although it is not authentically transmitted, there is no harm in saying it.