How do I migrate block content from a dev to a production site?
Another answer I haven't seen mentioned here is to use the Simple Block module, which is pretty much identical to core's 'Custom Block' setup, but instead of having a weird hybrid of content + config, you have all the Block settings and content stored in configuration, which can be cleanly exported and imported.

See, for further discussion in Drupal 8 core: Custom blocks cannot be properly exported and imported.