Hide video playback controls during presentation?

Hi, I've got a question about video playback during Keynote presentations.

I have a number of presentations that include fullscreen video slides. Keynote handles them really well and playback goes very smoothly, as long as I never move my cursor on the screen that's playing back the presentation. If that happens, a timeline with playhead and shuttle controls appears at the bottom of the video. No problem so far, that's fine. The issue is that these controls never hide themselves, no matter how long I keep my hand off the mouse, even if I move my cursor off the screen. And of course, anywhere I click outside of the controls advances the slide.

Is there any way to permanently hide the playback controls on a video? Any other workaround?