Getting people from popular Facebook page onto a group?

So I own a Facebook page with 220K likes that has a bunch of viral videos on it. I stopped posting on it for the last 6 months at least ever since I heard the news that Facebook is de-emphasizing non-friends posts. Well I check on my page recently and was shocked to learn that at least one of my old videos is currently going viral. A new video I posted got 20K views which is not bad.

Anyways, I was wondering what's the best way to get these fans to join a Facebook group? I heard groups get better reach than pages. I was thinking I could mass message people who comment on my page.

Invite them to the group. Come up with creative ads that can catch their attention. After all, you can let them enter a group without their permission.