Shuffling alphabet cipher
So, I found a way to do it but it's neither elegant nor a general solution. It relies on the (heavy) assumption that the initial chosen keyword is English and a second assumption that the resulting cipher text is also English. It then becomes a relatively crude bruteforcing exercise:

1) Choose an English word

2) Create a cipher instantiated by that word

3) Decrypt the ciphertext using that cipher

4) Check whether the decrypted plaintext contains English words

Using a relatively large wordlist (400k), it took around 30-40 seconds to break, the keyword itself was 9 chars long. As such, the solution would be completely unpractical if the keyword is random (which incidentally is the second part of this challenge and as such I will update this answer if I solve that one too).