Migrate content alone
You might want to take a look at Workspace, which which was added to Drupal core (8.6.0) just a month ago. It's mainly about content moderation and let's you prepare content on one site that then can be published to another site.

So maybe, if you wanna stick to your setup of one live (master) site and multiple dev (slave) sites, then you could let Workspace push just the content from live to dev – if it works this way.

Unfortunately, I can't find any really good documentation about Workspace. And yes, it has been added to core as an experimental module. But I'd say, you should give it try and can maybe contribute your experiences back :)