You can also rack mount "workstations" from HP and Dell.
The downside is that they are 4/5u. But they are a fucktonne quieter than server hardware.
The difficult part is getting the HDMI/DP extenders to work reliably or low latency enough without spending $2k.
Having said all that, Jeff's approach is most likley cheaper, if more fiddly. its certainly neater and more compact.