And as it happens, I was able to slide those filters out and brush them down in a sink-full of warm soapy water, and that did the trick. The water turned black (yuck), the filters came out shiny (woohoo), and the room with the aircon on no longer smells like motor oil (wtf?!). Damn fiddly getting the filters back in though. A lot of bad words were said.
Every "how to clean your air conditioner" resource on the internet seems to suggest doing - at least something - with the big motor part. I couldn't make out what. But, yeah, not needed this time around. Woo!