On this topic, I have thought that it might actually be a solution to the nuclear waste problem, to vitrify the stuff, and put it at the bottom of deep shafts drilled in a subduction zone, because you would be mailing it to the center of the earth, more or less.

If you chose your location on the subduction zone carefully, avoiding places like the Cascades, where the dropping plate makes some volcanoes and burps some of the subduction material back up relatively soon, the vitrified waste might stay down for a long time.

Does any lizard have a geology answer on how long a complete loop back tot he surface might take from a relatively quiet place on a subduction line?

If the time is significantly longer than the longest half lives of the stuff you are trying to get rid of, this burial method might work.