You've got the basic procedure right, but maybe not the diagnosis.

Usually you get a more of a whine from a differential than a hum. And I translate "in all probability" from a mechanic as "we don't know, so let's start by replacing the most expensive part."

I would get the car up on a lift or stands and have listen with a hose to my ear or one of those stethescopes before replacing the differential.

I personally would suspect CV joints or tire noise before the differential.

This is a tough one. Good luck.

__________________
Chuck Taylor
Falls Church VA
'66 200, '66 230SL, '96 SL500. Sold: '81 380SL, '86 300E, '72 250C, '95 C220, 3 '84 280SL's '90 420SEL, '72 280SE, '73 280C, '78 280SE, '70 280SL, '77 450SL, '85 380SL, '87 560SL, '85 380SL, '72 350SL, '96 S500 Coupe