You can't clear a heater to cathode short, no matter what you do. No
commercial CRT restorer even attempts it. If you try to discharge a
current through the short, you will kill the filament. The only
solution is to provice a "floating" heater source that won't drag the
cathode low when the contact is made. The heater voltage will
actually rise to cathode voltage (above ground), but will remain 6.3
between the filament pins. One method is to buy an isolation
transformer from supply houses, which is basically a toroid with two
windings on it. The other is to manually wrap some wire around the
flyback core, and feed to the filament. In either case, the CRT board
must be modified to float the filament pins completely away from
ground. Very common procedure done at repair shops.