Hi Max,
The typical use for this is certainly described in this document:
https://help.maxon.net/#49938
It is for sculpting, but a great source.
More to the point, (scroll down to displacement):
https://help.maxon.net/#TBAKETEXTURE-ID_BAKEOPTIONS
Note that there is also an option to bake Normal Maps, I guess you have seen the new series, but as he mentioned, that series is based on Windows tech only. Normal maps can only create an illusion of details, they won’t show up in the “silhouette”. If Displacement and which form (Intensity [centered], Red Green, RGB (O; T; W) will work with UNITY is not clear to me. You need to consult your client what they like to get. Note: The manual states: If you want to bake a displacement (only 3 types: Intensity, Intensity (centered) and Red/Green), a ,ray cast’ technique will be used.
I’m not certain what you object is and how it would translate with Displacement Baking. While considering a box, … but well you wrote already, that no option mentioned above is suitable.
BTW.:
For best quality, use for all information channels (vs. image channels, but there 32bit/channel float can’t hurt!) the best possible bit depth for color. I prefer 32bit/channel float and linear for these channels, for me always Open EXR. If they like a different format, from Open EXR 32bit/channel float and linear, everyone can get a clean lower quality image/map. If dumbed down from the start already to an integer format and sRGB (the smallest gamut), then chances are great that things might “go south”. C4D is internally working in 32bit/channel-float-linear, so why bother to convert and lower the quality while things are moving inside of a pipeline? With 8bit/channel one might get even dithering into the mix: Not nice.
Talk with the people who have to work with the material. A color profile translates the pixel information into a certain color space, and sRGB is certainly one of the lowest and should not be used during production. Any conversion into a new Colorspace will destroy the precision of information channels, clipping of values might occur. So keep the quality as long as possible on a top level.
My best wishes for the project