In any case you are left with no SSH, or somebody watching your ssh and have control over your ability to tunnel.
The best you can do with these boxes is make a sub tunnel over one of the protocols that they do allow through, you just can't rely on the primary encryption provided by the protocol that the middle box is executing MITM on. If somebody actually looks at the traffic they will see that you are not transferring plain text at the middle box, so that might raise some eyebrows.
While unfortunately for TLS client certificates are not a solution against MITM due to their awful user experience and privacy concerns, for SSH public key authentication has a good user experience, and is very common.