sounds to me like the throwout bearing is going out in your transmission. generally, the worse it gets, the more often
you will hear it. And the most common test to see if the throwout bearing is bad is to depress the clutch (like you stated)
and it generally goes away. to better determine this, get your car on a lift, with someone up in the car, have them hold the
rpms where the noise is constant, and listen from under the car, and i would bet that it is coming from the bellhousing area.
the part itself is fairly cheap, but it is the labor (if you choose to have someone else do it) is what will be slightly costly.