I have a friend who did similar tunneling a while ago. It also works on cruise ships.
He discovered that on some airlines (I think American?), they use an advanced fortinet firewall that doesn't just look at the SNI -- it also checks that the certificate presented by the server has the correct hostname and is issued by a legit certificate authority.
My friend got around that restriction by making the tunnel give the aa.com SNI, and then forward a real server hello and certificate from aa.com (in fact I think he forwards the entire TLS 1.2 handshake to/from aa.com). But then as soon as the protocol typically would turn into encrypted application data, he ignores whatever he sent in the handshake and just uses it as an encrypted tunnel.
(The modern solution is just to use TLS 1.3, which encrypts the server certificate and hence prevents the firewall from inspecting the cert, reducing the problem back to just spoofing the SNI).