I spoke too soon!
I dug around and it turns out Little Snitch 5 (released in 2020) provides a command line utility "due to popular demand".
You have to explicitly allow it in Little Snitch.app > Preferences > Security
.
From there you can add this to an Execute a Shell Script action:
sudo littlesnitch write-preference networkFilterEnabled false
or to re-enable:
sudo littlesnitch write-preference networkFilterEnabled true
You will have to run it as root, which is tricky (and risky) but doable. See this discussion.