Do it the right way and pull the keys. I know it takes a while, but that's the only way to do it with keyboards as dirty as this 
I took a run at it, as fast as I could.
Didn't take pictures as I was in a hurry and the keys all look pretty much like those Ripster posted in the M4 article.
What worked best for me to get the keys off was to use a hooked paper clip on a corner, jiggle it a bit, don't force too, just switch corners & keep trying, doesn't take too much effort. Oh, need to take some extra special care on the keys with stabilizer bars (all the larger keys). The bars all connect to the keys towards the "top" or "back" of the keyboard, and connect to the keyboard towards the "bottom" or "front" of the keyboard. So what I did was carefully pry the key loose by the top corners then detach them carefully making sure to disengage the stabilizer bar correctly without breaking the tiny mounts. If you don't think that you can be this careful and hold your force in check, might be best not to try removing these keys.
I cleaned it, not 100% but got most of the crap off. There was some dried crusty crud, several chunks of black plastic in there, some crappy dirty dust bunnies, and a rusty paper clip trapped under the spacebar. Some of the stabilizer bars, especially the spacebar one, had more then their share of dried crud on them, etc. Besides being gross, this stuff could mechanically impact the function of the keys.
I rushed the reassembly and must have gotten some moisture in down in the case as some of the keys weren't working correctly. As I have no idea how to open the case to do anything about it, I removed the keys and left it this way overnight to allow any possible moisture to dry out as there seems to be quite a bit more open space for evaporation with the keys off. I put the keys back on and at least in an initial test all keys work now.
Overall questioning if it was worth the effort. I don't think I would want to clean up something this bad all that often. There are still spots where there is some gunk residue, hopefully sanitized by lysol

, but it's minor and doesn't look obvious since it's all black.
Here are a couple of pictures with the keys off and rubber domes on. I believe all the domes are the same except the blue one under the space bar.

