I would think about this differently. What if the actual space inside these black holes does not stretch as the Universe itself does? The density relative to that of the Universe would increase, but they just maintained the density they originally had.
Thinking about a piece of fabric stretched with a mass on, as you drag the corners out, the curve (gravity) on the fabric (space) caused by the mass increases. If you locked the mass depth, it would look like it has gotten heavier.