So the insidious bug of Chrome on Android, which started in version 40, has now infected FireOS 5.1.1, which has upgraded its WebView to Chrome 41 (Samsung's 5.1.1 is still on Chrome 38 and does not have the bug).
As such, I was now kinda forced to find a workaround, so it is now out there. It turns out the bug only impacts Constant Bit Rate (CBR) files, and cases where there is no duration because it is a live-stream (e.g., transcoding down). Variable Bit Rate (VBR) files, like those from Amazon and Google Play are not affected because they actually specify a duration in their metadata.
In any case, I now have a workaround that seems to work, doesn't break the FireTV, and doesn't affect situations (like VBR, or like Firefox which calculates a duration from, well, somewhere) where the bug was never really present.
HTML5 is fun. Really.
Uploaded to the web and submitted to Amazon. Chrome desktop is not affected, so it has not been updated.
Joe