Although I'm not familiar with afxext.h, I am wondering what about it makes it incompatible with Windows NT4....
However, to answer the original question: "My research to date indicates that it is impossible to build an application for execution on Windows NT 4.0 using Visual Studio (C++, in this case) 2005."
The answer should be yes especially if the application was originally written or running on NT4! With the afxext.h thing aside, this should be an easy YES.
The other thing I am finding trouble with is the loose nature in which people are throwing out the NT term. Granted most people think of 'NT' as Windows NT4 but it's still ambiguous because 'most people' is not equal to 'all people.'
In reality the term 'NT' is equal to the NT series. The NT series is NT3, NT4, NT5 (2000, XP, 2003) and NT6 (Vista).
Win32 is a subsystem which you target your C/C++ code too. So I see no reason why one should not be able target this NT4 platform & subsystem or, if this is a platform porting excercise, remove the MFC dependencies that VC is possibly imposing.
Adding the afxext.h to the mix, it sounds to me like a subsystem compatibility issue. It's part of MFC from my Google research. The afxext.h appears to be the MFC (Microsoft Foundation Class) extensions.
Can you remove your dependency on MFC? What type of application is this? (CLR, service, GUI interface?) Can you convert project to an unmanaged C++ project in VC 8.0?
Hopefully some of this will help you along.