Kia Soul 2013, Strange Humming noise diagnosis.

We have a 2013 Kia Soul, I am not sure what the trim is, and it has been making an unusual noise while driving. We have taken it to three different mechanics, and have gotten three different answers as to what the problem is, so I am hoping to get some advice on diagnosing it.

Description of the noise:

1. It is a low pitched humming noise that increases in pitch with speed.
2. The noise is related to the speed the car is moving, and not engine RPM.
3. It is consistent and does not sound particularly like grinding. There are no clunking noises.
4. The car sometimes vibrates unsuslly briefly upon starting and at idle, but it is not consistent.
5. It sort of sounds like it is coming from the font of the car, but it is very hard to tell.
6. Turning left or right does not change the sound, but slowing down to turn lowers the pitch and volume the same way it would while moving straight.

What we have done so far:

1. Brought it to a local mechanic. Charged 200 to diagnose, they said the wheel bearings were fine, and that the sound was from a rock in the wheel. Rock was removed, sound remained.
2. Had all the wheels and breaks replaced as they were getting old anyway. They said the bearings were perfectly fine as well.
3. Had the dealership check it out while they were doing another bit of maintenance. Charged 200 to diagnose again, and they "recommended" a complete replacement of the transmission among other things to totally replace, and quoted $7000 to have it done.

Obviously I don't want to put that much money into a car that is not worth that much, but also I am not sure they even actually checked anything at the work order gave literally zero details about why they were recommending the transmission be replaced. That lack of disclosure and the fact that the sound does not sound much like bad transmissions I have heard in the past made me suspicious of their proposal. It might be true, but I do not want to take them at their word.

I know that the Kia Soul 2013 has an unusual transmission/differential where they are all built in together, so in my dumb-with-cars brain I think it might be what would normally be a problem with the differential, but I do not understand cars at all.

So I lack the context to know whether we should be looking for a new car now, or if there is something I can do to potentially rescue it.