How dense can storage get?

James Pitt has an interesting if not terribly useful post at Quora comparing the Bekenstein Bound, the absolute limit that physics places on the density of information, with Harvard's DNA storage experiment. He concludes:

the best DNA storage can do with those dimensions [a gram of dry DNA] is 5.6*10¹⁵ bits.

A Bekenstein-bound storage device with those dimensions would store about 1.6*10³⁸ bits.

So, there is about a factor of 3*10²² in bits/gram beyond DNA. He also compares the Bekenstein limit with Stanford's electronic quantum holography, which stored 35 bits per electron. A Bekenstein-limit device the size of an electron would store 6.6*10⁷ bits, so there's plenty of headroom there too. How reliable storage media this dense, and what their I/O bandwidth would be are open questions, especially since the limit describes the information density of a black hole.