At this point, it is speculation that the judge would not be impressed. If anyone decided to test the theory, the public would be informed regardless.

I agree, but your analysis is missing something: the canary-threatener may be secretly, without a public ruling, within the refresh interval, be convinced that if he doesn't keep updating (falsely) the canary, he'll go to jail. In other words, the precommitment to stop producing the canary signal isn't fully credible (though it seems much more likely to get the message out than a promise to actively say if something happens).

The technical solution to that social problem (yeah, we know how well those work) is to set the refresh interval to be less than the time required to process a motion contesting the government's order to update the canary.