The sae here, I also did not find any carbon rods big enough in diameter to use for my Gray tube project. I had to work whit what I had - a carbon rod from a 1.5V cylinder battery, it is 8mm in diameter. But I think that Beshires1 is right, because you can get much bigger pieced of carbon from motor brushes
Also thank you for your summary, lust like Greg, I finnaly understood what you mean when you say that the high voltage actually goes through the diode. And the analogy with the compressed baloon is great, makes sense to me This is exciting.