Don't laugh, this is an honest question.
Has anyone ever tried getting a dementor to suck the soul out of a Horcrux? That is hhow dementors "eat" after all. If a dementor sucks the soul out of the Horcrux, you don't have to go through the rather messy job of destroying the object. And, in the case of Moldywart's Horcruxes, you'd be able to save some very valuble objects.