Mac mini (Late 2014) second monitor

You can indeed use both the HDMI and Thunderbolt ports to drive two separate monitors with a Mac Mini.

Any Mac with a Thunderbolt port can use any mini Displayport display, cable or adapter, so you're correct that the mDP to DVI adapter is what you need¹. If you have a display that requires dual-link DVI (typically only monitors with resolutions higher than 1920x1200), you'll need an active mDP to dual-link DVI adapter.

For the HDMI port, HDMI to DVI adapters are readily available (HDMI is essentially a superset of DVI with a different connector). Note that the HDMI port is limited to monitors with 1920x1200 or lower resolution.

_{¹ Note that the reverse is not true - Thunderbolt monitors can't be used with mDP equipped Macs.}

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.