how is the shift into third gear(Drive) when cold? The hi-drum is used for both third and reverse. So if hi works fine, then
Yes I would do a band adjustment first. But since is is noisy, chances are that the lining is possibly gone, and you will see it as soon as the pan is off.
The Reverse servo gets full pump-pressure, usually about 250 psi, so if the band doesn't apply properly, it is usually because the servo is out of travel, or the band is toast.
So time to take the pan off and look.
But if the rpm flares on the 2-3 shift, then the hi-drum is toast, and the trans has to come down