What a shame, Annie. I think the lack of response to your question is a sign that "only time will tell" whether the plant will survive.
I would give it some shade as the weather warms up, until you're sure it's making some new roots it probably won't take full hot sun. Early spring sun, probably ok but as it starts to leaf out, keep a sharp eye on it for wilting in the middle of the day. If it does start wilting give it a spritz or two with the hose, to mist the leaves. This is a technique for rooting cuttings in the ground too, misting them and keeping shaded until they show new growth. New top growth indicates new root growth.
But I surely would prune back the top, maybe leave only a couple of good branches, so in spring the leaves will make some food for the roots to grow back.
As for the roots that broke off, some tree peonies are grafted, so if they do sprout, there's no guarantee you'll get the same plant from those roots. I gave my daughter a nice dark red tree peony, and after it bloomed the first or second year, a sport appeared from the base of the plant with a flower of an entirely different color, rather an unsightly mauve/pink. That's when I found out that tree peonies may (or may not) be grafted.
