Maybe it's time to switch to a web 2.0 solution? I know that my browser does play the .mp4 file if I click to "download" it, but integrating it into the page without the requirement of Flash would be great.
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The current player is too old, yes. If you like, ask UraniumAnchor directly about what the plans are with that (I know it sounds stupid but I can't get him to respond so there's nothing more I can do).