Does the "new" unit have brand new gears and bearings, or is it just "new to you" as in a used assembly that you have just installed? A gear whine on a used unit is virtually impossible to correct, at least that's been my experience in the 55+ years I've been building rear ends. Once a wear pattern that makes a noise is established, there's virtually nothing that can be done to change it. Any adjustment you try to make can only make things worse. Unless it's making noises that change from pull to float to coast, pinion bearings probably aren't the problem. Rough carrier bearings cause a steady hum that doesn't change with load, and gets louder as speed increases.
OK- - - -just re-read your original post. A hum on acceleration only is probably a bad pinion bearing. The front bearing is fairly easy to change, only requiring the removal of the driveline flange and the bearing retainer. If you decide to change both pinion bearings be sure not to alter the pinion depth which is set by shims between the pinion carrier and the main housing.
Jerry
