Video player "blink" in HTML5

I have a lesson that consists of branching video--a clip plays, buttons appear, and based on the user's choice a different video clip (on a different layer) plays.  The "cut" between the video clips is hidden by the video going out of focus, a translucent box covering it, and, of course, the buttons.  This makes the transition from one clip to another almost seamless.

However, in the HTML5 version, on every single clip the "Play" button of the video (that is, the icon in the middle of the video itself, not a button I have added) flashes for a split second before the video plays.  This is jarring and wrecks the seamless effect. (This is in Chrome.  In Firefox, the video does not play at all.  But that's a subject for another post, I guess...)

Does anyone know if there is a possible workaround to avoid this?  (I'm afraid I may already know the answer...)