Thanks to everyone who humoured me. There are some great answers here and I really enjoyed the other alternative cooking suggestions (that now have their own thread) 
Our whitegoods specialist, @airedale actually applied his scientific approach to this strange question and wrote up a full article explaining how (and why) you can cook a salmon dinner in your dishwasher. It includes video footage and a recipe, so be sure to check it out.
Here’s the final result:
I’m awarding BS Buster badges to @gordon, @PhilT, @mark_m and @syncretic for their thorough research and reasoning. Nice work!
