This is what I ended up doing. I used HandBrake to reduce the video to a reasonable size and then just put the MP4 on the site like anything else. I guess I'm getting a little carried away with my "minimalist" attitude in this case, where I want the video to be super light. Looks like a 2 minute video is about 4mb. Not great but not that bad compared to other modern websites either.

This will work for now but my mind still wonders if there isn't a better way to reduce the size of these. I'll continue to experiment.