Transmission problem or something else?

It is nigh impossible to provide sugestions as we do not know the source of the noise. You need someone to test drive the vehicle and locate the source of the noise to understand the problem better.

Why do you assume you're going to get ripped off? Mechanics have it a lot harder than doctors and you don't accuse them of ripping you off. Doctors only have to learn two models in various sizes, and they never change.

You know we can't hear the noise over a computer, but a much more common cause is a noisy front wheel bearing. The type of bearing depends on whether it's a two or four-wheel drive, which you didn't state, but if you have to be moving before you hear the noise, that rules out the power steering pump.

Two ways to identify a noisy bearing are to listen next to them with a stethoscope while running it in gear on a hoist, or to use a "Chassis Ear". That's a set of six microphones that are clipped to suspect parts, then you switch between them while listening with head phones during a test drive. Be aware that many mechanics have never heard of this tool, but all new car dealerships have them, and suspension and alignment specialists use them to locate squeaks and rattles. You might be able to find this tool at an auto parts store that rents or borrows tools.