My numbers come from d'=1.000 and v=0.500c.
For that case, do you agree that the co-location event E has unprimed frame coordinates x=0.000 and t=0.866?
Do you also agree that, according to the unprimed frame, the light would have to be located at unprimed frame coordinate x=ct=0.866 at time t=0.866, which is event P2?
If so, then you are disagreeing with your own claim, "If C' and M are co-located, then the light pulse is at P1 and that is the only correct answer." Once you acknowledge that there can be more than one answer in SR, you should realise that your argument is not valid.
I have no idea what you are saying. If C' and M are co-located, the light postulate puts the light pulse at P1. That is the only correct answer.
Now, are you claiming the light pulse is at 2 different places if C' and M are co-located?