Thanks TrippyLighting for your earlier attempt to help me! The problem I encountered was intertwined with a couple of Fusion 360 bugs. The more fundamental issue is still there.
You're right, b.marchal88 will probably be helped by grouping using components as you suggest.
BUT....in general: if you need subtractive features then components are not the answer AFAIK. You CANNOT subtract from a component (splits, cuts, intersections don't work). And a component can only be converted back to a body, or rather a set of bodies, by un-editable copy-and-paste ops on all the contained bodies.
Funnily, there is a "Move to Group" entry on the right-click list of a body in the browser. This concept is entirely distinct from "Create Group" further down in that list. The former is I think a legacy concept relating to surfaces and direct modelling. (I don't even know how to create such a group!) The latter is the ability to group timeline features into a kind of subroutines (which btw also aren't easily editable which in practice is annoying).
The "identity crisis" problem is that you generally CANNOT generally create a stable identify with which to refer to a group or a set of bodies.
An exception is a singleton set, a single object (use "Combine" and create new object, this will avoid creating gazillions of downstream errors when say you're using a body resulting from a split type of operations -- no guarantees that the body that results from the split won't change ID later with trivial updates earlier in the timeline --- the "Combine" catches a single unstable ID).
The other exception is a component with its additional baggage of capabilities unrelated to a stable ID for a body or a set of bodies.
The "identity crisis" problem is almost a showstopper in my workflow and the only major problem in Fusion 360 that I've had a hard time compensating for. So I'm glad to see this discussed again!
The answer to the add-on question: it is not possible to add to a copy-paste (unless moving bodies into a component, where you can move one object at a time).
In my understanding, the simplest two kinds of grouping (for bodies and timeline) are both incompletely implemented at the fundamental level. It's exciting to think of pure solutions to this -- a pleasing subroutine concept will emerge and so on, but that's another story and would involve a basic redesign of Fusion 360 concepts.