After some time I've finally figured it out. Due to some incompatibility between the Linux version and Win32 binary the only place where ffmpeg is actually properly looking for those templates is
To that end I've created the following batch script and copied the ffmpeg's x264 templates to a subfolder .ffmpeg where my ffmpeg binary lives:
And that's it! Now ffmpeg thinks that the home folder is where it lives and I don't have to pollute my home folder with stuff that doesn't belong there.
You can download the latest FFMPEG binaries from here (you want the "static" version for this setup).