Matt's suggestion of adding unique, valuable and interesting contextual info around the video is a very good approach.
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Best posts made by danatanseo
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RE: If I enbed the same video from my YouTube account on two different websites, will I get a duplicate content penalty?
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RE: Google is indexing urls with parameters despite canonical
I believe the problem here is being caused by the fact that you are using relative, rather than absolute URLs for your canonical tag. I've seen this happen before on a site I was working on. Thanks to awesome suggestions from Moz Q & A from community member George Andrews (endorsed by Dr. Pete Meyers), we updated all of our canonical tags to be absolute URLs instead of relative URLs. This completely solved the exact problem you are describing.
Here's a link to that thread: http://moz.com/community/q/what-is-the-proper-syntax-for-rel-canonical
The best news is, it's a very easy, inexpensive and quick SEO win.
I love those!
Dana