What I think the pope should do:
1)  Remove Burke and order him, under the obedience he promised to Pope Francis, to retire and remove himself to a life of penance and seclusion.  If he refuses, remove him from the cardinalate, reduce him to the lay state and then ignore him.

2)  Have a "come to Jesus" meeting with the nights and remind them that those in solemn vows do have to follow directions from the Holy See and offer to dispense them from those vows if they wish, reminding them that according to their own rules, it would remove them from office.

3)  Ask them to decide if they wish to continue as an Order within the church or if they would prefer cutting all ties the the magisterium and if so, dispense all from their vows, laicise any priests and canonically suppress the Order.  Then move on.