Even though I have nearly 2TB of free space, I cannot get either Windows Server 2008 R2 or 2012 to install, I get an error that setup cannot find a partition with enough free space for temp files.  Is there simply a way to tell Windows to skip this check?

skipping a critical pre-setup check is rarely a great idea.

does windows setup display your disks and partitions at all?
it may be a missing storage controller driver, or, your existing disks are partitioned using filesystems that windows can't use (e.g. linux filesystems)

do you have any un-partitioned  (un-allocated) space available/displayed at all? (i.e, is the free space outside of a partition)

Setup doesn't get that far, as soon as I click the Install button from the autorun screen I get a popup telling me that it can't find a partition with enough space.  There are currently three logical disks.  One is a 2.2TB mirror, another is a 6TB stripe set, and I have another 1.8TB mirror.  All disk space has been allocated to partitions, all have much more disk space that setup claims it needs.  I updated my environment variables to point temp and tmp to my strip set which has about 4GB free but still no luck.

it sounds like Windows setup has not detected your logical disks, so maybe Windows can't detect any storage at all.
Have you tried loading the storage controller driver via the F6 feature?
http://technet.microsoft.com/en-us/library/jj134246.aspx