This is the correct answer. There's nothing stopping you from setting up a 16 bit protected mode descriptor in your GDT and using it. The issue was in thunking HANDLEs.

https://msdn.microsoft.com/en-us/library/aa384249.aspx

> Note that 64-bit Windows does not support running 16-bit Windows-based applications. The primary reason is that handles have 32 significant bits on 64-bit Windows. Therefore, handles cannot be truncated and passed to 16-bit applications without loss of data. Attempts to launch 16-bit applications fail with the following error: ERROR_BAD_EXE_FORMAT.