We have evaluated the situation and confirmed that this can't be done.
The transmit and receiving function of Bluetooth required the device to operate in different mode, and the paired devices will established a boss-subordinate relationship (Host device and Client device). When N3 receive a file from your mobile via BT, the mobile is the host device and N3 is a client only. Once the N3 entered a client mode, all communication and operation will be directed by the hosted device, the client will be forced to receive file and play along as the host device take charge. On the other hand, you can only change the output setting of N3 when the DAP is operated as host, since you are not allowed to change the host/client relationship in the middle of a connection, so we have no choice but to disconnect BT connection before we change the output option.
Sorry for the delay in coming back to you, I was told we can't do this immediately but I didn't find out the technical reason until recently.