Your thinking is correct, it is indeed running rich unless the carbon you saw was oilly rather than fluffy. If it was oily then it is pumping oil. A very weak ignition could be causing something similar.

Unfortunately I am not versed in your particular injection system, but the O2 sensor is indeed one possibility.

If this is a KE injection system, then you need to disconnect the EHA and see if the engine runs okay. If it's not a KE then I can't offer any knowledgable help. Sorry for my ignorance of the breed.

Good luck,