I want to clean under the bottom burr housing, as there seems to be some caked coffee at the base, is taking off this piece advisable? If so, how do I get it off?

You need to remove the bolt (13mm) and then the bottom burr carrier needs to be pulled out. Ideally you'd use a gear puller that can be fit, but lacking that you insert three metric machine screws (1.5" long) through the threaded holes (in the photo) and screw them in symmetrically to lift the carrier off the shaft. Go easy. There's a plate underneath that covers the upper shaft bearing and you'll scratch it with the screws, so it's a good idea to smooth the threaded ends of the screws. Good luck.

You normally wouldn't need to remove the lower carrier just for cleaning...use a vacuum if you must. The reason to remove it would be to replace a defective carrier, substitute a larger one (i.e. convert Mini 58mm to 64mm burr set) or replace the motor bearings.

I had forgotten about that trick. From the FAQ Removing Super Jolly lower burr carrier:

Paul_Pratt wrote:Jamming things in may cause damage to the shaft. An easier way is to use long bolts and tighten them in sequence. The bolts push against the main body and force the carrier off. The risk of damage is low because the amount of force required is very small.

See pics.

I've done this with a mazzer super jolly that looked much worse than your picture and it was not worth the effort. That lower burr carrier is not easy to remove. I may still have some pictures of how I did it, it involved purchasing some long bolts that matched the thread of the burr mounting holes.

Thanks this is helpful, I suppose I'll keep it where it is in terms of cleanliness and when take it off in the future if I ever need to.

I've used the trick Paul described on several grinders and it worked like a charm. There can be plenty of smelly gunk underneath especially if a previous owner used the black and shiny beans called 'Italian'or "French"roasts so I'd give it a go...