I am please to report a partial resolution for future inqueries.

I now can connect to the server through VI, and get as far as the next 
screen that asks you to "make a new project" or "connect to an existing 
web."

I was able to do this by removing all filters on the server in IIS.  You 
can do this by going into IIS --> Right click on server name --> 
Properties --> Edit... (under master properties) -->  Click on Filters tab

I would advise writing down which filters you have and their locations 
since I have no idea what the filters do.  Also I left the fpexedll.dll 
filter because I believe it's used for FPSE.

For reference, I had the following filters installed:

UrlScan
C:\WINNT\System32\inetsrv\urlscan\urlscan.dll
Priority High

sspifilt
C:\WINNT\System32\inetsrv\sspifilt.dll
High

Compression
C:\WINNT\System32\inetsrv\compfilt.dll
High

pwsdata
C:\WINNT\System32\inetsrv\pwsdata.dll
Low

md5filt
C:\WINNT\System32\inetsrv\md5filt.dll
Low

fpexedll.dll
C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\40
\bin\fpexedll.dll
Low

-Jon