I just finished liking the page.

I don't mean to be contrary to the needs of the page or your desires as the admin but I'm not certain where your unnatural fear of allowing YouTube videos to be posted on this site is coming from. In my experience facebook does a great job of minimizing the size of YouTube videos that display on their pages. When added, they are physically tiny in size and take up only the small amount of space, no more than the average photo uploaded. They only open to a larger state when clicked by and viewed an individual viewer but do not remain in that larger state. Once you refresh the page, or log out and log back in, you'll note that the videos have returned to their previous thumbnail size. I am only guessing here, that you are perhaps unaware of this fact.