I've got the fake-full-screen set up, but it doesn't quite behave the way I want it to:

When in actual fullscreen, the engine automatically syncs to the screen frequency (this is known as VSync and is of high priority to my program). The fake-full-screen doesn't do this.
In my case, setting fps_max to 60 is insufficient because I'm actually counting single screen frames. My timing would be off if there's just the slightest difference between the screen frequency and the 60 frames per second the engine is set to.
Is there a way I can enable VSync anyways?

In terms of the mouse/losing focus issue, the fake-full-screen does exactly what I needed it to do. In terms of framerate, it doesn't.