Another solution that we recently built is called EmbedLite.com. It's a drop-in replacement where you swap the youtube.com domain in your iframe with embedlite.com. That's all the requirements.

-- <iframe src="https://youtube.com/embed/..."
++ <iframe src="https://embedlite.com/embed/..."

It loads a thumbnail of the YouTube video (just like the player). When someone click on it, it loads the true YouTube player.