Cr*p. I just erased my post by mistake. *SIGH* Oh, well. It was too long anyway.Here's a quick recap:
GIA rates emerald as "medium" in terms of hardness, this is what makes it good for most everyday wear. However, it is only "fair" in terms of toughness (along with others like tsavorite, spessartite, rhodolite, opal, pearls, turquoise...) due to its tendency for cracking and breaking.
To your list of "NOs," I'd add "no steam cleaning."
I might even skip the toothbrush and opt for a rub (not a "scrub") with a cloth soaked in mild, soapy, warm water. Or, a soft make-up brush is a good option. Then, rinse in cool water and wipe dry with a lint-free cloth. Just remember, ANY soap will, over time, break-down any fillers present the gem. Don't be afraid to clean more frequently, as opposed to waiting so long that the build-up is too much for an effective gentle home cleaning. The good news is that colored stones do not attract grease and oils the way diamonds do.