This is an interesting take on the problem of dealing with cognitive dissonance and the backfire effect (a la Leon Festinger’s “When Prophecy Fails”) but it doesn’t address the trouble of nuance in terms of the ways in which people deal with “failure.” In other words, personal cognitive dissonance is not always specifically at fault when people choose to protect a worldview over the presentation of scientific facts.
What this means is that we must also be especially aware of the ways in which belief systems have, pardon the word but, “fail-safes” already built into them. This means that upending individual denial isn’t enough when their entire belief system has integral ways of explaining, rationalizing, and incorporating failures of the system back into the system itself. This is why, when presented with evidence contrary to their views, “believers” don’t examine and rethink their positions, rather, they default to the system’s method of reintegration. This is what your argument must target; the capacity of the system to reassert itself.
Short version: Down with the system.