[Username1]

I agree with Marty you should try turning the tube an all directions and try zapping it. But I think an hour or so with a good bright light, and carefully inspect the neck of the tube to see if there is anything visible as far as a shorting item goes..... Use an ohm meter too, check it to see if its short at 0v. operating voltage, or does it short only on full operating voltages. And at last resorts don't forget to remove the socket if the short is there at 0v. It could be a mechanical short outside the glass envelope.
I don't think I would do the 3,0000uf cap at 400V, you could weld with that much current. I would offer this: Tap the end of the tube, tap it harder, possibly vibrate it with a cell phone motor on the tube neck. And turn the tube, put the bad gun top, bottom. But I would still keep the gun horizontal, not lay the tube face up or down.
But that is just me. I got a lot of tubes going again with heating the tube, and wacking it good with a screw driver. Just don't break it, I bet you will run the possibility of making progress fixing this as long as you take your time and think it out.