If you did a big nuclear scale event, then showed how it was all a CGI etc lie, that would certainly open up some minds to reconsider other narratives and end the power of the brainwashing devices.
LSWH
At this point I don't believe that the nukes are real. It also follows the same pattern, this time from the 50s. Get people afraid of nothing, hype it up to eleven, and profit. Lots of bunkers and tunnels were constructed in the aftermath.
Top it off by lying about radiation dose limits, and remove many of the formerly available sources of uranium so that people do not anymore have a way of finding out.
What you said could indeed be something of the lines on how you break it.
The nukes are NOT real : if they were we won´t be able to see Hiroshima and N so green (with people and animals living there) today.