I think smoothing is a good idea, but what you really want is not volume preservation, but coverage preservation. By that I mean the only important bit is not to create any new pokethroughs when smoothing. So one possible idea would be to check after each smoothing step whether any vertex has wandered inside the original convex hull for its ring, and if so, push it out again, probably along its normal or something.

That said, if you only need a small number of smoothing steps, volume preservation might come close enough, and is certainly easier to implement.

Just some unorganized thoughts of mine. Don't put too much weight on them.

-- I'm not mad at you, just Westphalian.