With some help from another person, we figured out it was an issue of ordering the source files within the HTML file. I learned that browsers accept the first usable format, and their seems to be an issue with the .m4v file, so I started with the .mp4, then .webm. Here's the order that works in Safari (even on my iPhone 5), Firefox, and Chrome:
<video width="100%" height="400" poster="assets/img/myVideo.jpg" controls="controls" preload="none">
<!-- MP4 for Safari, IE9, iPhone, iPad, Android, and Windows Phone 7 -->
<source type="video/mp4" src="assets/vid/PhysicsEtoys.mp4" />
<!-- WebM/VP8 for Firefox4, Opera, and Chrome -->
<source type="video/webm" src="assets/vid/PhysicsEtoys.webm" />
<!-- M4V for Apple -->
<source type="video/mp4" src="assets/vid/PhysicsEtoys.m4v" />
<!-- Ogg/Vorbis for older Firefox and Opera versions -->
<source type="video/ogg" src="assets/vid/PhysicsEtoys.ogv" />
<!-- Subtitles -->
<track kind="subtitles" src="assets/vid/subtitles.srt" srclang="en" />
<track kind="subtitles" src="assets/vid/subtitles.vtt" srclang="en" />
<!-- Flash fallback for non-HTML5 browsers without JavaScript -->
<object width="100%" height="400" type="application/x-shockwave-flash" data="flashmediaelement.swf">
<param name="movie" value="flashmediaelement.swf" />
<param name="flashvars" value="controls=true&file=assets/vid/PhysicsEtoys.mp4" />
<!-- Image as a last resort -->
<img src="assets/img/myVideo.jpg" width="320" height="240" title="No video playback capabilities" />
</object>
</video>
Now, I'll have to re-check the encoding on the m4v file (perhaps an issue of Baseline vs Main, High, etc.).