A few days ago I started an informal "experiment" of trying to propagate from root stock. I had dug up a tree (an inground one) that was in a bad location, and in the process broke some of the roots. I wondered about propagating from pieces of root, so here's what I did: I put four pieces of root in small pots. Two were a little less than a centimeter diameter and 5-7 centimeters long. One of these I put with about half a centimeter or root showing above soil (at one end), and the other all under the soil on its side (shallowest part about a half centimeter deep). Both pieces had cuts in the root where they were severed (from the shovel, and from my shears). The other two pieces are just tangles of small hairy root bits (and I don't have much hope for those, but what the heck, it didn't cost much time or material to include them in the test). I used a mixture of peat moss and sand (about equal parts), mostly because I had it close at hand. All four are in bright shade. I'll keep the pots watered as I would a tree. I realize this isn't a careful experiment with controls and such, but I just wanted to give it a try and see if it's possible to get a tree this way. As the season progresses I'll report on what I see happen from it.
We've been burying in-ground trees so long that we get all kinds of root suckers popping up new trees, but I can't tell if that's from stem/branch tissue that gets underground from "vertical drift" and/or breakage, or if it can happen from roots. So, maybe I'll learn something from this test and maybe not... will let you know.
Aaron - I realize this post doesn't help directly with your question (at least not yet), but it's related anyway, and if my attempt eventually yields any result I'll let you know in this thread. (And apologies if the prior discussions among experts here have already provided answers to this sort of thing... I just started this test on spur of the moment and without any real premeditation... when I saw your thread here I figured it might be worth reporting what happens with my little test).
Mike central NY state, zone 5