There's quite a few ways to do this, but I would probably use busses with some adjustments.
I noticed you write...
"as soon as the scene starts the background music ducks out before the player is close to the object."
- Do you have attenuation on the non-background music? Ducking should definitely not duck, unless something is actually playing through it. Alternatively, you could try attaching a Wwise Meter to the non-background music bus, and then connect the RTPC from it, to the volume of the background music.
Another less "volume-based" solution could also be to set an RTPC based on how close you are to the non-background music and map it to the volume of the background music bus. This should work quite well, as the RTPC influence will only subtract volume from the background music's audio bus, and so you can still have like a volume control RTPC on it as well.
- You can do that by creating a new script, and in your Update() function, set the RTPC to the Vector3.Distance(transform.position, playertransform.position).
If you want to see how this could be implemented, then for the Audio Bus ducking solution you can check out the arcade machine in WAG, that does exactly the same for the main music when it plays. For the method of setting an RTPC in Update, there's a section in Wwise 301 that describes more about that.
Let me know if this helps!