Try smacking the nut with a socket first to break the initial bond.
If you are failing
Then find a gate/jaali welder and buy 2 pieces of metal about 1 inch wide and chunky too. Make sure one is longer than the other, approx one piece should be 14 inches and the other 10
Drill holes on ends of the shorter one, one hole in the longer one and one hole somewhat at its 10 inch or so mark.
This is to fashion a pulley holder.
Use nut and bolts as fulcrum and also gripping tooth.
Use tool in provided holes.
You can also find similar but weaker tools in motorcycle market, they use it to hold magneto in place.