We found the cause of the massive performance loss and wanted to share the results with the rest of the Tableau Server clients. The performance loss was caused by two Windows Server 2008 R2 settings. When we disabled them, the problems went away. The first setting is called 'TCP Chimney Offload'. The second is called 'TCP Auto-Tuning'.
We are also troubleshooting performance issues with Tableau 6.1.1, Win2008R2 64-Bit on VMWare. Severe performance issues with the optimization of an extract Testing disabling TCP Auto-Tuning, (TCP Chimney Offload was already disabled) and it appears to have resolved the issue. Thank you Mike for your post!