I came across another possible path to solve this issue. Besides the hard sided bar of soap container, a container for a deck of cards is also pretty close.

An Altoids tin is 4"x2.5"x0.75"

A standard deck of poker size playing cards is 3.5"x2.5"x approx 0.75"

There are some brands of playing cards that are sold in an unhinged tin. Just have to look around for them.