I have very similar problem . I have humming sound coming from front mostly driver side. Starts when car start moving and increases with speed not related with engine rpm. Brake calipers , rotors all new. I thought its wheel bearings. While changing brakes, took out front knuckles, bearings seemed good. no rust at outside. they were turning nicely and quietly and they were tight enough. And also realized its very difficult to press out front hubs from knuckles without machine shop press setup. otherwise I was going to change them.
Im thinking is it possible axle bearings making that noise?
I don't know much about if front drive automatic transmission if they have similar drives and pinions, but I had bmw before, when their real differential goes bad they make very similar noise.