I'll take a stab at this. It sounds like you may be using something akin to a common industrial robot to do your milling? My experience (as I recall) was that the machine frame (robot speak for machine coordinates) effectively changes each time you re-orientate the head, thus changing the relationship with the workpiece ( the object frame). And re-orientating the head in a robot to a known fixed position in the work space was a common way to re-align the machine.
In my workflow, this change was initially recognized in my CAM software by changing the settings for my machine set-up, i.e. as a 5 axis mill. Although I was doing primarily 3+2, it is still essentially 5 axis work and involves changing the construction plane relative to the object being milled. It was all about the machine settings in CAM and had little to do with changing the post (the change in relationship, head to object, is then recognized in the post). I've not done any milling in Fusion yet, so I don't know if this can de done, but I would look to machine set-up in the CAM portion of Fusion first to try to accomplish this.