Plug-ins for static hosting? Our local dev environment allows us to run a CMS like Craft but our (government) host is static only. We currently accomplish things with movable type 4, but would like something more modern. MT 7 costs $1000 a year, so that is right out.

Is there a plug-in for Craft that can export static html we can upload to our host?
Perhaps you could have a local/internal Craft install and then regularly run a script that crawls the site and saves all the pages as static HTML. Tools like HTTrack already do a pretty good job of this. 

Or there are static cache plugins like Blitz that you might be able to utilise. They’re designed for caching, but if you warm the cache you might be able to export the static files for uploading to your host. 

UPDATE: Blitz 3 makes this possible. Read the announcement at: 
https://putyourlightson.com/articles/blitz-3-embracing-the-jamstack