Isn't it thought that a black hole's mass is concentrated in the center in a miniscule volume, such that the mass is not distributed throughout the "volume" contained by the event horizon? I'm not understanding what density means for a black hole when it isn't known what's between the singularity and event horizon.
I think from the outside, it doesn't matter whether the mass is uniformly distributed throughout the volume or concentrated at the centre - you would feel the same force of gravity. (I'd be interested to hear if there is an experiment you could do just measuring gravity to differentiate between the two!)