Because the shrinkage is the result of the evacuation of moisture from the clay on a molecular level, I don't believe you can do anything to mitigate the change other than calculating the shrinkage of your clay body and oversizing each piece as necessary. You can hang them from high-temperature wire, but if you fill the void in the center with no room to shrink, they will break.
As a jeweler who specializes in carving stones which are as hard or harder than porcelain, I do not suggest making rings from hard materials. Metals bend upon impact and even just from pressure - most thinner bands will actually go oval over time just from daily wear. Hard materials are also brittle and very susceptible to fracture from even small impacts because they are unable to absorb that energy. I have made rings in a variety of styles from quartz, agate/jasper, and jades and they've all broken eventually.