Polite message to my supervisor
My experience is that emails are far less effective than face-to-face interactions. If you are at the point that an email is all you can do because the relationship is dysfunctional and you just want to get out of there, then a simple statement acknowledging the validity of the approach in general but not in this domain, with the reminder that you need to graduate in a bit, would do the trick. Your advisors have no interest in needlessly prolonging your PhD (at least unless they have a serious grudge against you). 

Dear X

Thank you for suggesting method Y. I think it's a potentially useful approach that I am happy to explore in detail; however, it would seem that prior work indicates that the approach may not be as effective as we believe in domain Z (see attached PDF of the study by Alice and Bob Smith on the topic). I will be happy to add a discussion on this to the thesis (in the relevant section), but I do not believe that running a detailed analysis will yield fruitful results given the current state of the art. 

Given that I have to submit my thesis in 6 months, I think that the best course of action would be to focus on the results we have now, rather than expanding in new, potentially unproductive, directions. 

Regards

Maryam