[Eric H]

Lets start at the beginning, you need to go back and replace the filter capacitors, the hum in the sound indicates they are not doing their job.

Not every electrolytic in the set is a filter for the low voltage power supply. typically capacitors C1 & C2 will be your main filter caps, they will be connected right after your rectifier tube or Selenium. (you do have a schematic?) I would start with them.

You can't test them with an ohmmeter, the normal failure mode of an electrolytic is to go open or lose capacity or be slightly leaky, not a dead short.
It doesn't take much to make your meter jump, especially if it's digital but that doesn't mean the cap is good, they can also leak between sections and cause all sorts of problems.

Step two, get rid of the black beauties, they absolutely will and most likely are the cause of your vertical failure.
Start by replacing every small (.001 or bigger) cap attached to the vertical osc tube and go from there, the ones with pf values are likely ceramics and will be OK.

Of course it couldn't hurt to check some voltages and see if you find something way out of whack. You could have an open resistor or bad vertical output transformer.

The vertical osc/output tube itself could be bad of course but the odds are against it, sub it anyway if you have one, swap with another from a different section if there's another with the same number.

Eric