You don't need that. TTL zero and dns query header IDs are enough. You could even implement a threaded chat, using the id as a responded-to sorting mechanism.

Also, TXT can contain binary data, and when using DNS over TCP is pretty much unlimited in frame size.

If you're using DNS over TLS (or HTTPS, whatever) to the origin, sure third parties are limited.

If you're doing DNS over TLS to a public resolver that then transmits to an origin, that resolver is a third party that can see requests and responses.