I paid some £500 more for the ticket than if I had flown EK or EY on the same route
You've got rocks in your head, mate. I'd fly (and have flown) KLM to Asia, but only when it's cheaper or with much better connections than the Gulf or Asian carriers.
Having said that, I sympathize entirely with your sorry experience at the carousel. I've posted about this before: why the hell can't the airline tell you on arrival that your baggage didn't make the connection? After all, they've likely known for many hours. Is it so difficult to have someone at the arrival airport print out a list and stick it on a noticeboard next to the carousel?
Anyway, I have a tip for next time. Why stand waiting at the carousel at all? Instead, go straight to the handling agent and file a missing baggage claim - avoid the queues (after all if your bag didn't make it, likely others are also missing). Then go back to the carousel, and if you're lucky, pick up your baggage. You can cancel the missing claim on the way out, or call/e-mail them later. If your baggage is not there, you've already done the paperwork, so off you go.