Hi Chuck,
I have seen the same failure in my 515A, and the cause was a failure of the EHT transformer resonating capacitor which became leaky after a few minutes. In the 503, this capacitor is C620 and it is wired across one of the secondaries. Its value is 0.01uF 600V so it's not a very common part, but you may try replacing this first.
The good news would be that the HV transformer is OK. Please let me know if this helps !
Joel Setton