My suggestion is a hybrid approach. Migrate to Groups.io - and back up everything some other place(s) as well. BGG would be my first choice for everything that can be backed up there (if it is not already).
I am confused about the "Small cost" that was mentioned. the front page of Groups.io says "Great for open source projects. - Groups.io is Free.
Have an open-source project and need a group to discuss it? Groups.io is great for those. Full Github integration keeps people up to date on the development of your open source project. Post using Markdown with syntax highlighting."
I'm fine with a Google Group as well, especially since it is free. I mean, monetarily free. ;) And I've already sold them my soul.
Basically, whatever the next step is, I just want to be a part of it. :)