Hi Tim,
As you have observed you need to do at least a "soft" delete to exclude those bodies or components from being calculated in the overall mass numbers. We don't have a way of classfying a type of component for exclusion in mass properties like, for instance, Autodesk Inventor which does phantom parts.
Unfortunately, at this time we don't do center of mass or mass moments of inertia calculations native in the product. We just give you the mass.
A workflow you might consider though to make exclusions for your mass calculations a bit quicker is to use soft deletion and selection sets. Soft deletes are a feature that shows up in the timeline. They can be suppressed and unsuppressed for actions done in the future (which might save some time)

If you grouped your excluded parts into a selection set that would make furture selections easier to exclude. Just reselect and unsupress the soft deletion feature.

Hope that helps a little.
Best,
Mike
Michael Aubry
Autodesk Fusion 360 Evangelist