Even I suggested this method, I am actually on defense on the merit as well.

OP's case is in the grey area. So the chance of winning depends on the judge looking at the case (if OP indeed sues CX). Also - CX could settle this case before the trial.

Nevertheless - I can say with certainty that OP will not be able to obtain the refund with any traditional methods. So if OP is so desired to fight against CX, this method could work.