The cipher is an triple key polyalphabetic cipher also known as an Quagmire IV by the ACA. An example would be here: Quagmire IV example and info (pardon the ads)
I posses the IV key and the PT key. The IV key runs vertically and sets the shifts of the lookup alphabets for the ciphertext. The IV key is the length of the PT and is an plain English phrase. The PT key sets the shifts of the plaintext lookup alphabet. The length of the PT is ~120 characters, is in plain English and I possess an crib consisting of 4 letters and it's location in the ciphertext.
I have read and tried to adapt this method of solving a Quagmire IV but it deals with recovering the PT without the PT key but it does give insight. E.g. if we know the CT key and the IV key, the PT can be reduced to an simple substitution cipher.
I have attempted to attack the cipher using other methods used to solve polyalphabetic ciphers like Kerckhoff's principle and Kaliski but these and other methods I have used to solve simpler polyalphabetic ciphers have not yielded anything.
The question is what is the best manner of attack for this sort of cipher? Even the smallest bit of info about the CT key would be useful. E.g. if I found that the CT key length was 6, I could brute force it. I am not looking for solutions but more techniques/attacks that have some validity to them.
Edited for cipher details (below)
RXSF == THEY