So I tried again the "natural way" to solve this is Introjucer, by creating two configurations with the same name: "Debug" and "Debug". One is set to 32-bit and one is set to x64.
This is actually pretty close to working already. What happens in Visual Studio is that you get the proper combobox where you can choose "Win32" or "x64" within one single "Debug" configuration. And when you build the x64 version, VS automatically places all object files under "./x64/Debug" rather than under "./Debug".
However, the output binary is always placed under "./Debug", which confuses VS when trying to launch the x64 vs the win32 versions. If this little issue could be resolved, I think we would be there!
I guess it's all related to Introjucer setting an explicit output path, which is always "./Debug" or "./Release", but for x64 versions it should really be "./x64/Debug" vs "./x64/Release".
The workaround for this right now is to to set a custom Binary Location to "./Builds/VisualStudio2013/x64/Debug" in Introjucer on the x64 version of the Debug configuration, and a similar thing on the x64 Release configuration. So what should be "fixed" in Introjucer in my opinion is just a different Default Binary Location on x64 builds!