I'm no expert but think you have the set-up wrong; you have implied that you have the phone and headset paired, as well as each of them to the Nav 5.
I have an iPhone 6s directly paired to the Nav 5, and the Nav 5 directly paired to an F5MC headset (slightly different setup to you, but close enough I think to make no difference). My phone is not directly linked to the headset, so all inputs and sounds are managed via the Nav 5. I think your set-up is causing the F4MC to choose between the Nav 5 and the phone, causing the problems, whereas if everything is routed via the Nav 5 it can manage the switching effectively.
The only inconvenience is that I have to listen to music from the Nav 5, and updating tunes on that is a bit more of a faff than doing it on the iPhone.
Try binning the link between the F4MC and the phone and see if it all now works with the Nav 5 sat between them. Hopefully I've not misunderstood what you said...