Why does a class ring, spun like a top on its stone, stands up with the stone on the top?
You have given this more thought than I have, and a quick Internet search has left me high and dry about the typical inverting toy tops, a wooden sphere with a short dowel. I am also striking out with "class ring physics." I have sent a note to Jostens, one of the major purveyors of these rings, and I will let you know if they have any help to offer. [No reply]
Meanwhile, I do have some information to stir into the recipe.
Unless you went to MIT* or some other institution that doesn't use a stone, the stone has a third or less the density of the metal. (Quartz D= 2.7, Silver D= 10.5, Gold D= 19.3, many gems are based on quartz or closely related to it.)
As to how it would behave in microgravity, I can only speculate, although with all the personnel who have flown to space, I suspect someone must have tried spinning her or his ring! It would be difficult, if not impossible, by hand, to get a pure spin on the axis of the stone or axis of symmetry of the ring. Therefore, I would wager that the ring would appear to rotate as you have described, but I would also be willing to bet that it won’t exhibit any preference for a particular orientation. NASA had a "Toys in Space" program, and I hope they took a tippy top.
Having just remembered the expression, "Tippy Top," I discovered this amazing page of information. http://www.yorku.ca/marko/ComPhys/TippyTop/TippyTop.html I am afraid that you will have to explain to me what it means beyond about the third paragraph. :)
*My dad's "Brass Rat" is too worn to spin well, but he doesn't recall seeing MIT class rings stand up as you describe.
