The statement is that the explosion will happen “if the pole fits inside the barn” But we have to ask from whose perspective it fits and the physics would suggest that it must be from the perspective of the rider on the pole because the sensing mechanism to trigger the explosion must in effect observe if the pole fits and we know from the math that the observer on the pole will never come to that conclusion – hence no explosion.

Yes, but light is more practical

I think this is a good approach. All my life I have experienced the opposite method of derivation first and I am comfortable with that, but I can see the benefit of your approach.