What about starting a new root system with a ground layer using a tourniquet?
That should work provided the trunk is alive right round. Need to check to find out what has killed those other roots.
A ground layer will probably give better results than just chopping roots back but, again, you'll get far better roots on the layer if the tree is strong and healthy.
I spent some time root pruning more tridents from the grow beds - some smaller, some larger.
Here are just a few of today's trees: