How to use 3 DVI displays with new Mac Pro (Late 2013)
After more playing around, I now have a workaround whereby using a Mini DisplayPort to VGA adapter instead of one of the Mini DisplayPort to DVI adapters, i.e. an analogue connection to one of the displays instead of digital, seems to work and allows me to have 3 active displays configured like so:


  Display 1 connected via HDMI to DVI adapter (into HDMI port)
  
  Display 2 connected via (passive) Mini DisplayPort to DVI adapter into
  Thunderbolt port 5 (as in the diagram in the above article)
  
  Display 3 connected via Mini DisplayPort to VGA adapter into
  Thunderbolt port 2.


However, I was hoping to have an all-digital solution as the above Apple article suggests I can, so I'm still hoping someone will come up with a better idea!



UPDATE: This appears to be an issue introduced with OS X 10.9.3. Tried an identical machine running 10.9.2 and the second configuration I tried in the original question worked just fine. Hopefully it'll be fixed in 10.9.4, until then the workaround above is still valid.