All good thoughts and questions John.Polarity was chosen as + to the copper, - to the Carbon. Per the practice described in the texts I found.
Good idea to try two carbons. I may spring for some better material. Pencil graphite may be too resistive, as there is clay added to the composition. A more massive metal electrode (not just wire) may also help, by conducting heat away.
The thought to try more inductance is a good one, and had already been considered. In fact one starting point may be to go for audible frequency - the "singing arc" - first and then try progressively higher frequency.
Best regards,
Ed