The schematic shows .1 ohms or less, you indicate .6, it maybe OK but, that is the winding not the filament inside the tube itself. Just check your solder connections, since it's a rectifier, the solder connections that are connected have to tolerate a lot of heat, so when you turn off the radio, the solder is being subject to temperature changes, that causes the solder to fracture and over a long time it will develop what is called a cold solder joint, so it's best to use fresh solder just to make sure.
If you have a cold solder joint the resistance increases, maybe that's why you're reading .6 ohms.
And yes you should read 0 ohms on the socket pin to chassis ground, which means that one side is good as far as continuity.
I would suggest you use a dim bulb tester in series, so it will limit the current, and not exceed your variac current. You can also check the filaments of each tube, just to make sure by doing a continuity (ohmage) test.
Have you replaced the power filter capacitors???
If not you may burn out the transformer. If you had to resolder the transformer, that is a concern of a previous short being developed by the caps as mentioned. But my not being there is a guess as to why the repair.
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