EAX vs CTR vs XTS + cascade ciphers in disk encryption hell
This would allow my system to stay secure even if one of these ciphers has been broken, right?


Most likely, however one can construct situations where the cascade is only as strong as the first cipher.


  If so, EAX is arguably better than XTS, isn't it?


It is.


  Are there maturity issues?


No, it actually has a security proof for the strongest notion for a symmetric encrytion scheme, namely as an authenticated encryption scheme assuming the used block cipher is secure.


  Why is it so unpopular?


In general because AES-GCM / ChaCha-Poly1305 is faster with similar security properties. In this specific case of disk encryption because it incurs 16 bytes of overhead per authenticated message. These 16 bytes are really annoying in disk encryption. They mean that either the disk encryption software has to offer a smaller, non-standard sector size which may not be supported by the OS or it has to remove a linear amount of storage from your disk as well as completely break most performance assumptions by requiring two sector accesses by logical sector access. 

Most people are not willing to sacrifice ~1% of their disk space and take the high performance stemming from the extra sector accesses for a defense against a rare attack scenario of manipulation attacks.


  Is it possible to use a more sophisticated hashing algorithm like bcrypt instead?


Theoretically? Absolutely. Practically? Your disk encryption software simply has to support it.