I'm looking for an extension that will either add a YouTube searchbar to Speed Dial (preferably) OR something where I can replace the google (or other choices) search engine search with YouTube. I've looked in the extension repos, but can't seem to find one that does what I'm looking for.
You can not do what you ask because, in general, you can not set a custom search engine as the default and thus have it appear on spped dial.
However, you can add youtube's search as a custom search engine. Right click on youtube's search field > create search engine > fill the details there > done.