I've thought about the same thing. The Octal 6SN7 and it's 9-pin equivalent the 6FQ7 would give better current drive than the 12AU7. The 12BH7 would also do the same. You'd have to tweak the heater voltage as they pull more current. And change the bias voltage a bit. Jim has a schematic somewhere in this Circle for the Octal Cornet that uses a 6SN7 for the cathode follower and you can reference that.
So far I've not made any changes and still use the AU7. Since its used as a cathode follower, I suspect an AU7 is just fine (or in my case a 5814). It works well for me with my set-up and my pre-amp input resistance is 22k so I don't think I'd benefit much from the extra drive of the SN7 family. But if you do go this route, I'd be interested in your findings.