That box simulator you linked does not consider the Thiel/Small parameters of your specific woofers, so it is too general to be of value to you. It probably uses math from the days before T/S were invented, or considered essential for speaker design. The T/S parameters should be used to determine the box volume for a high performance speaker design like you're planning if you want to get the full potential low frequency performance from the woofer. In a very small speaker like this you really don't want to leave any potential bass performance untapped!
The nominal parameters of the woofer are published by SEAS, but they do vary from sample to sample, and batch to batch, so it is good to measure your own actual drivers, after break in, if possible. If you don't have a tool
to measure driver specs then you can use the factory specs.
A good free box simulator which factors in the Thiel/Small specs and can also simulate passive radiator is WinISD.
Make sure to use the newest version 0.7. The passive radiator also has some T/S specs to use in WinISD, though without a motor it has less specs than the woofer.
PS - When designing your crossover, don't forget to incorporate baffle step correction.
This is something often neglected by new speaker designers, but a small box like yours will be sorely lacking in bass without baffle step compensation. The BSC is the reason the Harbeth has only 83dB sensitivity, but it's also why it has decent bass for such a small speaker. The WinISD simulator does not factor in box diffraction in the FR simulation. BSC is traditionally considered part of the crossover design, even though it is closely related to the box dimensions.
If you want to continue using your Speaker Box Volume Calculator, then you can fudge the box a little bigger than it recommends, then put some solid blocks of foam or wood inside the box to reduce the volume if necessary when you are fine tuning the design. It's easier to make the volume smaller than to make it bigger.
Which woofer and PR are you using?