Do not soak the Chosera, it is against the manufacturers recommendation. choceras-cracking-t5748.html
The Green Brick is basically splash and go, so I would wet as needed to use, then wipe down and air dry, but this is just my opinion.
I wonder if someone could set me straight: I generally try to soak my stones a little a possible. For my Nubatama Umes, I have been giving the about a 2-3min soak, so I don't begin soaking the 2k until I am already using the 1k. The Arashiyma I do the same, begin soaking while using my 2k stone. The rest of my line up is splash and go, so I do not soak. Then I towel dry my stones, set them on my cooktop grate and leave them there to air dry till I need to cook next, usually the next afternoon. When I store them, they are in a tupperware box that I leave the top off so they can breath. I only just got several of these stones so my habits have not been put to the test, but my King Ice Bears have been treated like this for ~4 years and I have not had any problems.