How to find out the maximum footprint height of NOT the tool, but everything gantry?

I’m planning the mpcnc primo right now, and I want to have a Z-axis of 200mm. I plan to build a flip table with the machine in a box with a lid.
I am aware that with 200mm Z-axis the footprint height will be 640mm.

However I don’t want to build a box to that full height, but build a box only as high as it has to be for the gantrys / rails / motors on the sides.

I will then have a lid, with a little tower somewhere to encapsulate the tool.

Therefore I need to know the minimum height my box needs to be, in order to encapsulate the side rail components.

How can I find that out?
Because it influences if I even go for 200mm, if that box height is still a lot more than 300mm.

Thank you for your time