The lead (plumb) box would definitely help in reducing the effect of cosmic radiation.
Now, if I believe everything I learned during my B.Sc., the optimal location on where to store the film is in a place where the effort needed to get it is lowest... but I should add that I got my diploma in Town Planning so that's not very good for film
But on a more serious note, professional films are designed to be optimal at the moment they are shipped. So, keeping at a constant cool temperature is best. Film degrades in many ways. There is the background radiation which affects it and the only way to prevent this is a box with a heavy lead liner. The freezer won't protect against this. But the freezer will slow down the internal chemical reactions which slowly cause the film to degrade. Also, degradation speed is not constant. Film changes chemically faster when fresh simply because there are more molecules in it that can react with one another than when it's really old.
As for the gelatin, this fears mostly humidity and high PH which will cause it to soften. It's not as sensitive to fungus as we might think as it is laced with formaldehyde to both harden the gelatin and prevent bacterial or fungus growth.
The best thing to do is freeze the stuff and allow it to thaw about an hour before putting it in the camera. When in a hurry, I just heat the can in the palm of my hand until it's not very cold. I never had a problem with that.
On the up side, B&W film is not as affected by aging as color stock (degradation is not as visible since there's no color to judge)
The only thing is that film degrades much faster once it's exposed. The molecules have gathered the minimum amount of energy needed to transform into a different compound and become slightly unstable.
(BTW, I have a backup Instax...
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