Ok, seems like it may have resolved. I re-installed the plugin and got new API keys and Access tokens. Published a post and voilà!
No idea what could’ve caused it.
Tried that just now. Added “Tweet when edited,” saved settings. Created a new post, and still no Tweet.
1) Yes the WP to Twitter meta box is visible.
2) No errors appear when I publish a post.
3) Settings are configured in Basic Settings that posts will be Tweeted.