I'm pretty sure aerographite is porous, and the numbers you're quoting don't count the mass of the air permeating the aerographite. You could wrap it in something like mylar, but it'd be less safe than helium. Any break in the skin would be like a hole in a space capsule. This could be ameliorated with smaller cells, but that cuts into your lift. It's also not clear if aerographite is strong enough for the job.

To make something as safe and reliable as you describe, you'd have to build an evacuated closed-cell foam. That material would have to be extremely light while also being able to withstand being crushed by the atmosphere. It's not clear if anything is up to the task.

Sorry to dash your hopes.