Let me preface this reply by saying I in no way approve or condone the poor and inconsistent customer service responses that some posters in this thread have received!
However, I think that mrtdxb's advice is sound and will do much more for your happiness than getting additionally stressed or dwelling on a service failure for too long. Definitely send in the complaint, then do what you need to do, whether that's cancel all your tickets, post on flyertalk, etc. etc. - waiting for a response that will probably not come, or if it does, be insufficient to assuage your now amplified unhappiness due to the compounded irritation of delays, is just wasting your own time and energy I think. From the airline's point of view, threats to move business are heard thousands of times a day - and most of those are probably acted upon. But for every person who vows never to fly with EK again, you have people who have done the same for QR or EY or LH or BA or whichever airline: the actual demand for air travel between various points has not changed and so in the end, x amount of people and cargo need to get from a to b in z amount of time. There's only so much capacity and scheduling that is available and I think airlines know this. And so customer service is going to be a department that will chug along doing what it does until there's a noticeable effect on revenue and load factors that they can pinpoint due to customer service. Which I have to admit in the history of the airline industry is going to be really unlikely. People keep flying. They grumble, but they pay the money. The accounts that EK really want to keep? That's what commercial account managers and iO status is for.
In the end, regard your complaint as a rant to get off your chest and regard compensation or even acknowledgement as a bonus and you should have fewer grey hairs: it's not about "letting EK off the hook", it's about your own mental wellbeing. After all, who's going to win in an emotional battle, you, an individual who feels a sense of being aggrieved, or a faceless corporation that just doesn't care? There are better battles to fight, I think...!