Using groups may be part of your problem. . You can use layers, names and colors to create subsets of surfaces for IGES export. Also it is a good idea to join all the connected surfaces which have the same color. If surfaces are joined in Rhino (open polysurfaces) that also will organize the surfaces in the IGES file.
There are lots of options for sending color and surface information via IGES. I’ve been sending color information by IGES to CAM and CAD programs for about 18 years and never had a problem. You can also do the same thing to send color info by STEP format.
Also in Rhino you can accurately compute the volume of a closed polysurface even if you separate it into color coded parts. So you can extract surfaces from a closed polysurface and group the components by joining surfaces that you want connected and assigning colors and still get the same volume calculation as long as you select all the parts that make up the closed polysurface.