What I would do if I were you is use the original title you were going to use on the YT video & page, and then on the site use a relevant near duplicate title or one that integrated other niche targeted keywords. Then if you can have the video transcribed into text you can put this text on your site and it technically is more robust than the YT page and video. Your effectively competing on authority with Youtube and quality content on your own site, which you leave it up to the algo to put the most relevant piece of content up highly, and after a couple of weeks should be the most robust content on your site that has lots of text content (video transcription), relevant images, and other links pointing out to high authority 3rd party sites as Google likes to see that sites that "spread the love".
I get this question quite often in the digital marketing firm I work at. But yes you can outrank Youtube just don't expect it to happen in 24 hours unless your CNN, Techcrunch, etc.
Hopefully this was of help.
thanks that was quite enlightening