I can't tell as much from the pictures as I would like, but it appears that the trunk just snapped in two?

If it were me, I'd cut the trunks without foliage down to about 1" from the top of the ground. Leave the one(s) that didn't break off. The tree should send up new shoots, and with luck, some should be from the root or from below ground level. Don't remove any of the new growth during the first year. The tree will need all the foliage it can produce to overcome the tramma. Starting the next year, remove undesired growth so that no more than about a third of the foliage is removed per year. Select a trunk, or trunks, that originate from the roots or from as low as possible on the trunk. Within 2 to 3 years, you should be able to narrow the shoots down to only the ones you want. It may take some time, but eventually the tree should grow back.

Yikes!.....I meant "trauma".

Good advice.
We did something along that line to regrow a tulip poplar with an 18" diameter (a tornado torqued the top so badly that it dropped out). The chosen tree is back up to fifteen feet now.
My one question is...is there rot where the tree snapped off or even termites? If so, the problem needs to be cleaned out/killed so that the replacement has a better chance.