I'm looking for some re-assurance

I don't think the calculations regarding size/height/volume require much accuracy, anyway.
The critical thing is that, whatever the amount the system installs, the water/chlorine ratio has to be right.
As long as that ratio is correct, it doesn't matter that the system thought it delivered enough to restore the height to 6 inches, but in fact delivered only enough to restore the height to 5 inches.
So ... all you really need to closely monitor is the amounts of water and chlorine that are injected (and for simplicity, I'd be measuring those in ml, not cubic inches).
If they are disappearing in the right proportions; the tank level never drops below a quarter full; and the level gets restored to at least, say, two thirds full (without overflowing) then all is good.

I think your arithmetic is well within those bounds.

Cheers,
Rob