It is my experience and uderstanding that these are called suckers and that they will never become trees like the orginal tree WAS. They will get very very bushy and will not be as strong either.
They will not live too long either.
What I would do in the mean time is to find one particular off shoot or sucker that looks strong and straight and manicure it to become nice and pretty. Cut off all the others and let the energy go to that one particular off shoot that you want to develope.
The life expectancy of willows are not that long compared to oaks or other trees. They require soo much water intake that they live naturally near or touching rivers, streams, lakes and other bodies of water.
The suckers are living off the roots of the mother tree that are still alive and not giving up on life.
Since it is such an old tree and the root system probably goes many feet deep and many many yards out from the center, there is not much you can do to treat the tree. It will do what it needs.