Good luck. That particular tube is known for premature green cathode
short failure. Virtually every one of that tube of that vintage I have
seen in the last 5 or so years has all been bad in the same way.

Why is the tube bad in this one?
If it is the common cathode to heater short, a manual method of
removing the short may work.

IMHO that particular tv model is not worth putting $400 into it. $400
would go a long way towards buying a like new but used Sony tv set in
that size that does not need repair.