AppleScript-sent messages pop up as unsent drafts when trying to quit Mail
D'oh! Finally figured it out, and it's all my fault. Setting visible:true is the key. The problem was that I was always editing the original scripts in my ~/Library/Scripts/ folder, but testing them by using the hot key I set up to trigger...duh...the Automated workflow files in ~/Library/Services, which I had not updated.

Posting an answer in case someone else does something as dumb as I was doing. /headdesk