Not a physicist and hate to nit-pick, however.....
I think the inverse square law of which you speak actually has very little effect in reducing the radiation dose between concorde altitudes and boeing altitudes.
The reduction is due to the attenuating affect of the thicker layer of atmosphere above the boeing, compared to the concorde.
Does anyone know what the day / night variation is in radiation dose? I've always assumed i was not being slow cooked at FL410 at night, in the earths shadow. Is this a correct assumption, or is there some perverse reason why it doesn't work like that?