It doesn't seem like it's possible if you don't use the HTML <video> element in your custom implementation. Even the Youtube API states:
Although the AS3 player supports playback speed controls, currently variable speeds are only supported in the HTML5 player.
Currently (May 2015), it’s best to create your own solution, since youtube seems to use flash memory even in some browsers that support html5 video, for example, my Opera 29 (although if I change my user agent to chrome , it really serves the html5 player ...). Most browsers can handle mp4, and you can encode video from different playback speeds as a backup if the <video> element is not supported. At the moment, <video> support is approaching 95% in the US , so there’s no need for your audience.
Another point in favor of using your own solution is that youtube seems to only support playback up to 2x speed (200%).
The biggest problem with posting your own video, which is not allowed by the <video> element, as I saw it, is loading on the server. Using a CDN is likely to solve this problem. Please note that my laptop cannot play smooth hd videos (well, DVD quality, I don’t have a lot of videos to test), which comes from my own machine more than 2 times, so if you don’t use very small videos you may find 10x impractical.
HTML5 Rocks has a good overview of customizing the <video> element.
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