What was your XMPP client connecting to? Was it a well-known public endpoint (that they could be whitelisting) or was it a private server? If the latter then that indicates that they are allowing arbitrary IP connections which in theory means that you should be able to proxy any traffic you want. I doubt they are doing DPI, since TLS makes this very difficult these days when you don’t control the certificate stores on the clients.
I’d imagine they’re relying on some combination of DNS whitelisting and port blocking which should be trivial to circumvent if you know ahead of time what traffic they allow through.