I have 2 suggestions:
1. Longer term but safer: Leave the roots alone this winter and get the tree healthy through next summer then chop if everything is doing better next winter.
2. Quicker but more risk: Chop the strong roots by about half of the old section. If it survives that the lack of roots should get some new roots growing nearby. Make sure the roots are well covered with potting mix through summer. Roots cannot grow if they dry out each day.