My knowledge of apparmor is basic unfortunately. In particular, interaction with dbus is something I never looked at before UT, and bluetooth and network management with apparmor is totally unknown to me.
Yes my suggestion of using network bluetooth was not very well thought out, I was believing that maybe there was special in associating the two, as if there was a right called network_bluetooth. My bad 
This said, there is something that bothers me in your log: it suggest that there is a denial in the sending FROM the server (the systemd service) TO your app. Usually when a sending is denied, it is the sender that is lacking rights.
So following this idea, it could be the system itself that is missing a configuration. However, see above, I have no idea how rights are managed for the bluetooth services.
Maybe all that is needed is to add an apparmor profile for the obexd executable, but often the obvious solution is wrong.
Note that if you want to test it, there is no need to turn your rootfs r/w, with overlay or bind-root you can 'add' stuff in read only directories.
Sorry not to be more specific, but going deep in system administration takes time and concentration and I'm currently in other stuff.
