Here is the white mold. Close up, it looks a bit like wisps of cotton.
The good new:
The rind is drying out and the cheese is firming up!
The even better news:
It appears that the orange mold has stopped spreading. (You can see it above, on the top edge in the foreground, getting covered over with the fluffy, white mold.)
I did end up removing most of it tonight. The mold became less cute and fluffy, and slightly grey and dingy looking. Most of it came off with a gentle brushing.
(There is a dark grey/black mold that grows off the sides of cheese, called 'poile de chat' - cat's hair. It is usually found on goats' milk cheese, so I am pretty confident the mold on cheesie is a type of penicillium... but I am not 100%)