Well that 10 000c thing is a bit far feched. Carbon, being the most refractory element in the periodic table, having boiling point of around 5000c l think. Yes for a short period of time l guess it is possible but not in a long run.
On toughening, as l understand, with cheramic wool (aluminium silicate) you add aluminium hidroxide and sodium silicate between the fibres and when they heat up form aluminium silicate between the fibres, glueing them together with the same material.
But you made me think, what if cheramic fibres were mixed with this diy starlite? My guess is as the carbon foam starts to form it shuld capture fibres in the structure making it stronger?