If there are scheduled messages queued to be sent when Thunderbird starts up, then Send Later sends them immediately, before the user has a chance to click any "Stop" button. The only way to prevent that is to delete the message when you no longer want it sent, which is what I explained to the user.
There's also a preference the user could have enabled in the Send Later preferences to tell it not to send messages that are past due by more than x minutes when Thunderbird starts up. So there are actually _two_ different ways already in the extension for solving the problem the user wanted solved.
It's FOSS, I don't have unlimited time to work on it, there are a lot of other more important features I'd be working on if I had time rather than adding a third solution to a problem for which there are already two other solutions.