The error was caused by where I was placing the rc.exe and rcdll.dll files. Because I'm compiling to a 64-bit platform, Visual Studio is using the 64-bit 'cross-compiler' which does not reside in the C:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin but in the C:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin\x86_amd64 folder.
Thus, the solution to my problem was to copy rc.exe and rcdll.dll from the C:\Program Files (x86)\Windows Kits\8.1\bin\x86 folder to the C:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin\x86_amd64 folder.
Doing that overcame that first error.
However, upon building, a new error popped up: LNK1158: cannot run 'cvtres.exe'. In contrast to my first rc.exe error, this file actually already does reside in the C:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin folder. The problem is that the cross-compiler is looking for it in its own directory. So I just copied that file from the C:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin folder to the C:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin\x86_amd64 folder.
Once I did that, my project built and ran.