Jason:
I think you've confused the C2 with the A2 which will never support this feature:
https://community.extremenetworks.com/extreme/topics/c2_b2_a4_a2_series_has_ssh_session_error_nonexi...
The C2 within its own release notes says that in version 5.02.16.0008
they believe the issue was resolved, though it doesn't seem to be. Note below our revision number: (connected using Netsight)
And now the error by connecting from Putty rather than Netsight:
I've figured out why launching SSH via Netsight works, apparently they've built in version 0.60 of Putty into Netsight which didn't suffer from this issue.
So I think in short, the rather annoying workaround is to launch SSH via Netsight for the C2s. This way you can continue to use the latest and greatest for Putty for unaffected hosts and keep the benefit of SHA-256 instead of being forced down to SHA1 at best no matter your host's capabilities.