How does an atom's electronegativity change as it becomes more negatively charged?
Electronegativity is a measure of the ability of an atom to attract electrons to itself (usually in a bonding framework; outside of a bonding framework the ability to attract electrons is electron affinity). 

So from simple Coulombic considerations, we can surmise that as your carbon becomes more and more negatively charged, the less it will be able to attract electrons to itself.