Matrix is decentralized, using centralized auth wouldn't work.
You could even host your own matrix homeserver to talk in that room. (like email, or XMPP)
It would be easy to move. Just upload the web site files to a Github repository with index.html in the root path, and turn on Github pages in the setting tab.
Other benefits that immediately come to mind are: - Anyone can submit suggestions, these are called Pull Requests. - Eventually you can add trusted community members as collaborators and they can edit pages directly. - There is already a massive community that know this interface. - It's free for public sites. - Last but not least, it's super easy to edit the site, just do it directly in the browser, no need for builds, deploy scripts, etc.
I checked out riot.im but honestly I found the interface really confusing. Also, the lack of integration to a major auth service like Google/Twitter/Github/etc is a real turn off for me.