I think if the boost capacitor had gone short the PY500A would be glowing. I would check to see if there is any line drive.
It's a long time since I worked on one of these, but if there are any of those clear plastic cellophane capacitors in the oscillator I would replace those first.
The PL509 could be faulty I suppose, it's worth trying another. You could also try disconnecting the tripler in case the load is excessive.
The line transformers were quite reliable on these sets but I remember replacing a few when the sets got old, It seemed that a faulty tripler was more likely to kill the transformer when the sets had a lot of years behind them.
I really liked these hybrid ITTs. They had a very long service life and outlasted many of their peers like the Decca 30 and Pye 697.
The 22" in particular was very kind to its tube and many were well into their teens with the original Mullard A56 120x.
They were more reliable than many of the next generation of solid state colour sets
I can count the common faults for the CVC5/9 on the fingers of one hand, now try that with a Ferguson ICC5 or a G11 !