I think that making empirical tests would be easier than applying any measurement someone could give you.
I will say this... I did an experiement where I had 2 films sandwiched together (screen-plate w/ slide film) and it was difficult to get it in my ordinary holder. So, it must be right around or slightly less than double the thickness.. .014 +/- (mm, inches?). I sanded out the channels with some fine grit sandpaper and now they both fit nicely.
Any slop in the holder with regards to it's "vertical" movement up in down in the channels won't really affect performance and i don't think that it will fall out as long as it's caught on at least 3 edges. (at least with ≤5x7" I should think)